| Records |
| Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
| Title |
n-ary algebras: a review with applications |
Type |
Journal Article |
| Year |
2010 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
| Volume |
43 |
Issue |
29 |
Pages  |
293001 - 117pp |
| Keywords |
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| Abstract |
This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. 3-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. As a result, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations ( it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A(4) model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization. |
| Address |
[de Azcarraga, J. A.] Univ Valencia, Dept Theoret Phys, Fac Phys, E-46100 Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es |
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Thesis |
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| Publisher |
Iop Publishing Ltd |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
1751-8113 |
ISBN |
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Expedition |
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Conference |
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| Notes |
ISI:000279463100003 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
no |
| Call Number |
IFIC @ elepoucu @ |
Serial |
419 |
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| Author |
de Azcarraga, J.A.; Gutiez, D.; Izquierdo, J.M. |
| Title |
Extended D=3 Bargmann supergravity from a Lie algebra expansion |
Type |
Journal Article |
| Year |
2019 |
Publication |
Nuclear Physics B |
Abbreviated Journal |
Nucl. Phys. B |
| Volume |
946 |
Issue |
|
Pages |
114706 - 14pp |
| Keywords |
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| Abstract |
In this paper we show how the method of Lie algebra expansions may be used to obtain, in a simple way, both the extended Bargmann Lie superalgebra and the Chern-Simons action associated to it in three dimensions, starting from D = 3, N = 2 superPoincare and its corresponding Chern-Simons supergravity. (C) 2019 The Author(s). Published by Elsevier B.V. |
| Address |
[de Azcarraga, J. A.] CSIC UVEG, Dept Fis Teor, Valencia 46100, Spain, Email: azcarrag@ific.uv.es; |
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Thesis |
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| Publisher |
Elsevier |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
0550-3213 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000487935600012 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
no |
| Call Number |
IFIC @ pastor @ |
Serial |
4156 |
| Permanent link to this record |
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| Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
| Title |
k-Leibniz algebras from lower order ones: From Lie triple to Lie l-ple systems |
Type |
Journal Article |
| Year |
2013 |
Publication |
Journal of Mathematical Physics |
Abbreviated Journal |
J. Math. Phys. |
| Volume |
54 |
Issue |
9 |
Pages |
093510 - 14pp |
| Keywords |
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| Abstract |
Two types of higher order Lie l-ple systems are introduced in this paper. They are defined by brackets with l > 3 arguments satisfying certain conditions, and generalize the well-known Lie triple systems. One of the generalizations uses a construction that allows us to associate a (2n – 3)-Leibniz algebra pound with a metric n-Leibniz algebra () pound over tilde by using a 2(n – 1)-linear Kasymov trace form for () pound over tilde. Some specific types of k-Leibniz algebras, relevant in the construction, are introduced as well. Both higher order Lie l-ple generalizations reduce to the standard Lie triple systems for l = 3. |
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Place of Publication |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
0022-2488 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000325407300032 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
no |
| Call Number |
IFIC @ pastor @ |
Serial |
1618 |
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| Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
| Title |
On a class of n-Leibniz deformations of the simple Filippov algebras |
Type |
Journal Article |
| Year |
2011 |
Publication |
Journal of Mathematical Physics |
Abbreviated Journal |
J. Math. Phys. |
| Volume |
52 |
Issue |
2 |
Pages |
023521 - 13pp |
| Keywords |
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| Abstract |
We study the problem of infinitesimal deformations of all real, simple, finite-dimensional Filippov (or n-Lie) algebras, considered as a class of n-Leibniz algebras characterized by having an n-bracket skewsymmetric in its n-1 first arguments. We prove that all n > 3 simple finite-dimensional Filippov algebras (FAs) are rigid as n-Leibniz algebras of this class. This rigidity also holds for the Leibniz deformations of the semisimple n = 2 Filippov (i.e., Lie) algebras. The n = 3 simple FAs, however, admit a nontrivial one-parameter infinitesimal 3-Leibniz algebra deformation. We also show that the n >= 3 simple Filippov algebras do not admit nontrivial central extensions as n-Leibniz algebras of the above class. |
| Address |
[de Azcarraga, Jose A.] Univ Valencia, Dept Theoret Phys, E-46100 Burjassot, Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es |
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Thesis |
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| Publisher |
Amer Inst Physics |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
0022-2488 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
ISI:000287811800050 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
no |
| Call Number |
IFIC @ pastor @ |
Serial |
558 |
| Permanent link to this record |
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| Author |
de Azcarraga, J.A.; Izquierdo, J.M.; Picon, M. |
| Title |
Contractions of Filippov algebras |
Type |
Journal Article |
| Year |
2011 |
Publication |
Journal of Mathematical Physics |
Abbreviated Journal |
J. Math. Phys. |
| Volume |
52 |
Issue |
1 |
Pages |
013516 - 24pp |
| Keywords |
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| Abstract |
We introduce in this paper the contractions B-c of n-Lie (or Filippov) algebras B and show that they have a semidirect structure as their n = 2 Lie algebra counterparts. As an example, we compute the nontrivial contractions of the simple A(n+1) Filippov algebras. By using the. Inonu-Wigner and the generalized Weimar-Woods contractions of ordinary Lie algebras, we compare (in the B = A(n+1) simple case) the Lie algebras Lie B-c (the Lie algebra of inner endomorphisms of B-c) with certain contractions (Lie B)(IW) and (Lie B)(W-W) of the Lie algebra Lie B associated with B. |
| Address |
[de Azcarraga, Jose A.; Picon, Moises] Univ Valencia, Dept Theoret Phys, E-46100 Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es |
| Corporate Author |
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Thesis |
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| Publisher |
Amer Inst Physics |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
0022-2488 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
ISI:000286898400034 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
574 |
| Permanent link to this record |
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| Author |
Camarero, D.; de Azcarraga, J.A.; Izquierdo, J.M. |
| Title |
Bosonic D=11 supergravity from a generalized Chern-Simons action |
Type |
Journal Article |
| Year |
2017 |
Publication |
Nuclear Physics B |
Abbreviated Journal |
Nucl. Phys. B |
| Volume |
923 |
Issue |
|
Pages |
633-652 |
| Keywords |
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| Abstract |
It is shown that the action of the bosonic sector of D= 11supergravity may be obtained by means of a suitable scaling of the originally dimensionless fields of a generalized Chern-Simons action. This follows from the eleven-form CS-potential of the most general linear combination of closed, gauge invariant twelve-forms involving the sp(32)-valued two-form curvatures supplemented by a three-form field. In this construction, the role of the skewsymmetric four-index auxiliary function needed for the first order formulation of D= 11supergravity is played by the gauge field associated with the five Lorentz indices generator of the bosonic sp(32) subalgebra of osp(1|32). |
| Address |
[Camarero, D.; Izquierdo, J. M.] Univ Valladolid, Dept Fis Teor, E-47011 Valladolid, Spain, Email: j.a.de.azcarraga@ific.uv.es |
| Corporate Author |
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Thesis |
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| Publisher |
Elsevier Science Bv |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
0550-3213 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000413405200028 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
no |
| Call Number |
IFIC @ pastor @ |
Serial |
3333 |
| Permanent link to this record |
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| Author |
de Azcarraga, J.A.; Izquierdo, J.M.; Lukierski, J.; Woronowicz, M. |
| Title |
Generalizations of Maxwell (super)algebras by the expansion method |
Type |
Journal Article |
| Year |
2013 |
Publication |
Nuclear Physics B |
Abbreviated Journal |
Nucl. Phys. B |
| Volume |
869 |
Issue |
2 |
Pages |
303-314 |
| Keywords |
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| Abstract |
The Lie algebras expansion method is used to show that the four-dimensional spacetime Maxwell (super)algebras and some of their generalizations can be derived in a simple way as particular expansions of o(3,2) and osp(N vertical bar 4). |
| Address |
[de Azcarraga, J. A.] Univ Valencia, Dept Phys Theor, E-46100 Burjassot, Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es |
| Corporate Author |
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Thesis |
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| Publisher |
Elsevier Science Bv |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
0550-3213 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000314562600007 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
1324 |
| Permanent link to this record |
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| Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
| Title |
D=3 (p, q)-Poincare supergravities from Lie algebra expansions |
Type |
Journal Article |
| Year |
2012 |
Publication |
Nuclear Physics B |
Abbreviated Journal |
Nucl. Phys. B |
| Volume |
854 |
Issue |
1 |
Pages |
276-291 |
| Keywords |
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| Abstract |
We use the expansion of superalgebras procedure (summarized in the text) to derive Chem-Simons (CS) actions for the (p, q)-Poincare supergravities in three-dimensional spacetimes. After deriving the action for the (p, 0)-Poincare supergravity as a CS theory for the expansion osp(p vertical bar 2: R)(2, 1) of osp(p vertical bar 2: R), we find the general (p, q)-Poincare superalgebras and their associated D = 3 supergravity actions as CS gauge theories from an expansion of the simple osp(p + q vertical bar 2, R) superalgebras, namely osp(p + q vertical bar 2, R)(2, 1, 2). |
| Address |
[de Azcarraga, JA] Univ Valencia, Dept Phys Theor, E-46100 Burjassot, Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es |
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Thesis |
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| Publisher |
Elsevier Science Bv |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
0550-3213 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000296167500011 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
no |
| Call Number |
IFIC @ pastor @ |
Serial |
787 |
| Permanent link to this record |
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| Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
| Title |
Minimal D=4 supergravity from the superMaxwell algebra |
Type |
Journal Article |
| Year |
2014 |
Publication |
Nuclear Physics B |
Abbreviated Journal |
Nucl. Phys. B |
| Volume |
885 |
Issue |
|
Pages |
34-45 |
| Keywords |
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| Abstract |
We show that the first-order D = 4, N = 1 pure supergravity lagrangian four-form can be obtained geometrically as a quadratic expression in the curvatures of the Maxwell superalgebra. This is achieved by noticing that the relative coefficient between the two terms of the lagrangian that makes the action locally supersymmetric also determines trivial field equations for the gauge fields associated with the extra generators of the Maxwell superalgebra. Along the way, a convenient geometric procedure to check the local supersymmetry of a class of lagrangians is developed. |
| Address |
[de Azcarraga, J. A.] CSIC UVEG, Dept Fis Teor, Burjassot 46100, Valencia, Spain |
| Corporate Author |
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Thesis |
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| Publisher |
Elsevier Science Bv |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
0550-3213 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000339598300003 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
no |
| Call Number |
IFIC @ pastor @ |
Serial |
1857 |
| Permanent link to this record |
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| Author |
de Azcarraga, J.A.; Fedoruk, S.; Izquierdo, J.M.; Lukierski, J. |
| Title |
Two-twistor particle models and free massive higher spin fields |
Type |
Journal Article |
| Year |
2015 |
Publication |
Journal of High Energy Physics |
Abbreviated Journal |
J. High Energy Phys. |
| Volume |
04 |
Issue |
4 |
Pages |
010 - 39pp |
| Keywords |
Field Theories in Lower Dimensions; Higher Spin Symmetry; Extended Supersymmetry; Space-Time Symmetries |
| Abstract |
We present D = 3 and D = 4 world-line models for massive particles moving in a new type of enlarged spacetime, with D-1 additional vector coordinates, which after quantization lead to towers of massive higher spin (HS) free fields. Two classically equivalent formulations are presented: one with a hybrid spacetime/bispinor variables and a second described by a free two-twistor dynamics with constraints. After first quantization in the D = 3 and D = 4 cases, the wave functions satisfying a massive version of Vasiliev's free unfolded equations are given as functions on the SL(2, R) and SL(2, C) group manifolds respectively, which describe arbitrary on-shell momenta and spin degrees of freedom. Further we comment on the D = 6 case, and possible supersymmetric extensions are mentioned as well. Finally, the description of interactions and the Ads/crr duality are briefly considered for massive IHS fields. |
| Address |
[de Azcarraga, J. A.] Univ Valencia, Dept Theoret Phys, E-46100 Burjassot, Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es; |
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Thesis |
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| Publisher |
Springer |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
1029-8479 |
ISBN |
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Medium |
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Expedition |
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Conference |
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| Notes |
WOS:000356852000010 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
2293 |
| Permanent link to this record |
