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General properties of the expansion methods of Lie algebras

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Autor Andrianopoli L.
Autor Merino N.
Autor Nadal F.
Autor Trigiante M.
Fecha Ingreso 2014-04-05T00:19:20Z
Fecha Disponible 2014-04-05T00:19:20Z
Fecha en Repositorio 2014-04-04
dc.identifier 10.1088/1751-8113/46/36/365204
dc.description.abstract The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also means that a new physical theory can be obtained from a known one. One of the procedures that allow us to do so is called expansion of Lie algebras, and has been recently used in different physical applications - particularly in gauge theories of gravity. Here we report on further developments of this method, required to understand in a deeper way their consequences in physical theories. We have found theorems related to the preservation of some properties of the algebras under expansions that can be used as criteria and, more specifically, as necessary conditions to know if two arbitrary Lie algebras can be related by some expansion mechanism. Formal aspects, such as the Cartan decomposition of the expanded algebras, are also discussed. Finally, an instructive example that allows us to check explicitly all our theoretical results is also provided. © 2013 IOP Publishing Ltd. en_US
dc.source Journal of Physics A: Mathematical and Theoretical
Link Descarga dc.source.uri
Title dc.title General properties of the expansion methods of Lie algebras en_US
Tipo dc.type Article

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