| 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 These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries.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 |
| Corporate Author |
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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 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 |
1751-8113 |
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:000279463100003 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
no |
| Call Number |
IFIC @ elepoucu @ |
Serial |
419 |
| Permanent link to this record |
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| Author |
Bandos, I.A.; de Azcarraga, J.A.; Meliveo, C. |
| Title |
Extended supersymmetry in massless conformal higher spin theory |
Type |
Journal Article |
| Year |
2011 |
Publication |
Nuclear Physics B |
Abbreviated Journal |
Nucl. Phys. B |
| Volume |
853 |
Issue |
3 |
Pages |
760-776 |
| Keywords |
Higher spin theory; Conformal field theory; N-extended tensorial superspaces; Superfield theory |
| Abstract |
We propose superfield equations in tensorial N-extended superspaces to describe the N = 2,4,8 supersymmetric generalizations of free conformal higher spin theories. These can be obtained by quantizing a superparticle model in N-extended tensorial superspace. The N-extended higher spin supermultiplets just contain scalar and 'spinor' fields in tensorial space so that, in contrast with the standard (super)space approach, no nontrivial generalizations of the Maxwell or Einstein equations to tensorial space appear when N > 2. For N = 4,8, the higher spin-tensorial components of the extended tensorial superfields are expressed through additional scalar and spinor fields in tensorial space which obey the same free higher spin equations, but that are axion-like in the sense that they possess Peccei-Quinn-like symmetries. |
| Address |
[de Azcarraga, JA] CSIC UVEG, Dept Fis Teor, Burjassot 46100, Valencia, Spain, Email: azcarrag@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:000295955100008 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
no |
| Call Number |
IFIC @ elepoucu @ |
Serial |
781 |
| 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 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: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.; 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 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: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 |
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 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:000339598300003 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
no |
| Call Number |
IFIC @ pastor @ |
Serial |
1857 |
| Permanent link to this record |
