SQG1 - Strings/Brane Motivated Gravity |
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Speaker |
Rodríguez, Eduardo |
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Co-autors |
Fernando Izaurieta, Alfredo Pérez, Patricio Salgado |
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Talk Title |
Expanding Lie and Gauge Free Differential Algebras through abelian Semigroups |
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Abstract |
The relevance of Lie algebras in physics can hardly be overemphasized. The Poincaré algebra, for instance, lies at the core of Special Relativity, and serves also as a local symmetry in General Relativity. Supergravity, on the other hand, lacks so far a clear-cut gauge theory interpretation, and this is often regarded as a major drawback. It is the purpose of this talk to introduce a method for the so called expansion of Lie algebras, namely the abelian semigroup expansion, S-expansion for short. For every Lie algebra g and finite abelian semigroup S, it is shown that the direct product G = S x g satisfies the requirements for a Lie algebra as well. When certain conditions are met, ``resonant subalgebras'' and ``reduced algebras'' can be extracted from the S-expanded algebra G. Crucially for its potential applications in physics (particularly in gauge formulations for gravity and supergravity), the method produces an invariant tensor for the S-expanded algebra G from one for the original algebra g. We also review the dual version of the method in terms of the Lie algebra's Maurer-Cartan forms. This dual version permits the generalization of the method to the case of a gauge free differential algebra, which is relevant again for applications in supergravity. |
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