Dual formulation of the Lie algebra S-expansion procedure

DOI10.1063/1.3171923zbMATH Open1256.17004arXiv0903.4712OpenAlexW2054391054WikidataQ115333469 ScholiaQ115333469MaRDI QIDQ4907602

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Publication date: 4 February 2013

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Abstract: The expansion of a Lie algebra entails finding a new, bigger algebra G, through a series of well-defined steps, from an original Lie algebra g. One incarnation of the method, the so-called S-expansion, involves the use of a finite abelian semigroup S to accomplish this task. In this paper we put forward a dual formulation of the S-expansion method which is based on the dual picture of a Lie algebra given by the Maurer-Cartan forms. The dual version of the method is useful in finding a generalization to the case of a gauge free differential algebra, which in turn is relevant for physical applications in, e.g., Supergravity. It also sheds new light on the puzzling relation between two Chern-Simons Lagrangians for gravity in 2+1 dimensions, namely the Einstein-Hilbert Lagrangian and the one for the so-called "exotic gravity".

Full work available at URL: https://arxiv.org/abs/0903.4712

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