Dual Formulation of the Lie Algebra S-expansion Procedure

Fernando Izaurieta; Alfredo Pérez; Eduardo Rodríguez; Patricio Salgado

doi:10.1063/1.3171923

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arXiv · 0903.4712

Dual Formulation of the Lie Algebra S-expansion Procedure

Fernando Izaurieta·Alfredo Pérez·Eduardo Rodríguez·Patricio Salgado

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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".

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Fernando Izaurieta, Alfredo Pérez, Eduardo Rodríguez, Patricio Salgado. 2009-03-26. Dual Formulation of the Lie Algebra S-expansion Procedure. https://doi.org/10.1063/1.3171923

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