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Expanding Lie (super)algebras through abelian semigroups

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arxiv hep-th/0606215 v2 pith:SRBOQZEW submitted 2006-06-21 hep-th math-phmath.MP

Fernando Izaurieta , Eduardo Rodríguez , Patricio Salgado This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords algebrasabelianalgebrasemigrouparbitraryariseauria-fre-likeazcarraga
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We propose an outgrowth of the expansion method introduced by de Azcarraga et al. [Nucl. Phys. B 662 (2003) 185]. The basic idea consists in considering the direct product between an abelian semigroup S and a Lie algebra g. General conditions under which relevant subalgebras can systematically be extracted from S \times g are given. We show how, for a particular choice of semigroup S, the known cases of expanded algebras can be reobtained, while new ones arise from different choices. Concrete examples, including the M algebra and a D'Auria-Fre-like Superalgebra, are considered. Finally, we find explicit, non-trace invariant tensors for these S-expanded algebras, which are essential ingredients in, e.g., the formulation of Supergravity theories in arbitrary space-time dimensions.

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Cited by 4 Pith papers

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  1. Non-Lorentzian Supergravity and Kinematical Superalgebras

    hep-th 2024-12 conditional novelty 7.0 of 10

    Supersymmetric extensions of extended kinematical algebras are classified via semigroup expansion, and non-degenerate Chern-Simons supergravity actions are constructed in three dimensions.

  2. On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

    hep-th 2019-08 conditional novelty 6.0 of 10

    New infinite-dimensional superalgebras, the deformed and enlarged super-BMS3 algebras for N=1,2,4, are produced by S-expanding super-Virasoro and are related by a flat limit.

  3. Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields

    hep-th 2024-12 conditional novelty 5.0 of 10

    The asymptotic symmetry algebra of three-dimensional Maxwell Chern-Simons gravity with spin-3 fields is a new nonlinear algebra, hs3max-bms3, which is also obtained as the flat limit of three copies of the W3 algebra.

  4. 3D Carrollian gravity from 2D Euclidean symmetry

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    Post-Carroll-Newtonian Chern-Simons gravities are systematically obtained by semigroup-expanding 2D Euclidean B_k algebras, recovering known Carrollian models as subcases.

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