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Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
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Title |
n-ary algebras: a review with applications |
Type |
Journal Article |
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Year |
2010 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
43 |
Issue |
29 |
Pages |
293001 - 117pp |
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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 These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries.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. |
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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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Publisher |
Iop Publishing Ltd |
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English |
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ISSN  |
1751-8113 |
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ISI:000279463100003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ elepoucu @ |
Serial |
419 |
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Author |
de Azcarraga, J.A.; Fedoruk, S.; Izquierdo, J.M.; Lukierski, J. |
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Title |
Two-twistor particle models and free massive higher spin fields |
Type |
Journal Article |
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Year |
2015 |
Publication |
Journal of High Energy Physics |
Abbreviated Journal |
J. High Energy Phys. |
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Volume |
04 |
Issue |
4 |
Pages |
010 - 39pp |
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Keywords |
Field Theories in Lower Dimensions; Higher Spin Symmetry; Extended Supersymmetry; Space-Time Symmetries |
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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. |
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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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Publisher |
Springer |
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English |
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ISSN |
1029-8479 |
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Notes |
WOS:000356852000010 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
2293 |
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Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
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Title |
D=3 (p, q)-Poincare supergravities from Lie algebra expansions |
Type |
Journal Article |
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Year |
2012 |
Publication |
Nuclear Physics B |
Abbreviated Journal |
Nucl. Phys. B |
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Volume |
854 |
Issue |
1 |
Pages |
276-291 |
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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). |
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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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Publisher |
Elsevier Science Bv |
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English |
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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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Area |
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Expedition |
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Conference |
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Notes |
WOS:000296167500011 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
787 |
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Author |
de Azcarraga, J.A.; Izquierdo, J.M.; Lukierski, J.; Woronowicz, M. |
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Title |
Generalizations of Maxwell (super)algebras by the expansion method |
Type |
Journal Article |
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Year |
2013 |
Publication |
Nuclear Physics B |
Abbreviated Journal |
Nucl. Phys. B |
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Volume |
869 |
Issue |
2 |
Pages |
303-314 |
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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). |
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Address |
[de Azcarraga, J. A.] Univ Valencia, Dept Phys Theor, E-46100 Burjassot, Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es |
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Publisher |
Elsevier Science Bv |
Place of Publication |
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Language |
English |
Summary Language |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0550-3213 |
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Medium |
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Expedition |
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Conference |
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Notes |
WOS:000314562600007 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1324 |
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Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
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Title |
Minimal D=4 supergravity from the superMaxwell algebra |
Type |
Journal Article |
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Year |
2014 |
Publication |
Nuclear Physics B |
Abbreviated Journal |
Nucl. Phys. B |
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Volume |
885 |
Issue |
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Pages |
34-45 |
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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. |
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Address |
[de Azcarraga, J. A.] CSIC UVEG, Dept Fis Teor, Burjassot 46100, Valencia, Spain |
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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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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 |
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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 |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
1857 |
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