Bandos, I. A., de Azcarraga, J. A., & Meliveo, C. (2011). Extended supersymmetry in massless conformal higher spin theory. Nucl. Phys. B, 853(3), 760–776.
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.
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de Azcarraga, J. A., Izquierdo, J. M., Lukierski, J., & Woronowicz, M. (2013). Generalizations of Maxwell (super)algebras by the expansion method. Nucl. Phys. B, 869(2), 303–314.
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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de Azcarraga, J. A., Kamimura, K., & Lukierski, J. (2011). Generalized cosmological term from Maxwell symmetries. Phys. Rev. D, 83(12), 124036–8pp.
Abstract: By gauging the Maxwell spacetime algebra, the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six four-vector fields A(mu)(ab)(x) associated with the six Abelian tensorial charges in the Maxwell algebra. In the simplest Maxwell extension of Einstein gravity this leads to a generalized cosmological term that includes a contribution from these vector fields. We also consider going beyond the basic gravitational model by means of bilinear actions for the new Abelian gauge fields. Finally, an analogy with the supersymmetric generalization of gravity is indicated. In an appendix, we propose an equivalent description of the model in terms of a shift of the standard spin connection by the A(mu)(ab)(x) fields.
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de Azcarraga, J. A., & Izquierdo, J. M. (2013). k-Leibniz algebras from lower order ones: From Lie triple to Lie l-ple systems. J. Math. Phys., 54(9), 093510–14pp.
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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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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