de Azcarraga, J. A., & Izquierdo, J. M. (2014). Minimal D=4 supergravity from the superMaxwell algebra. Nucl. Phys. B, 885, 34–45.
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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Camarero, D., de Azcarraga, J. A., & Izquierdo, J. M. (2017). Bosonic D=11 supergravity from a generalized Chern-Simons action. Nucl. Phys. B, 923, 633–652.
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).
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de Azcarraga, J. A., Gutiez, D., & Izquierdo, J. M. (2019). Extended D=3 Bargmann supergravity from a Lie algebra expansion. Nucl. Phys. B, 946, 114706–14pp.
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.
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de Azcarraga, J. A., Izquierdo, J. M., & Picon, M. (2011). Contractions of Filippov algebras. J. Math. Phys., 52(1), 013516–24pp.
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.
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de Azcarraga, J. A., & Izquierdo, J. M. (2012). D=3 (p, q)-Poincare supergravities from Lie algebra expansions. Nucl. Phys. B, 854(1), 276–291.
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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