English

Dual Formulation of the Lie Algebra S-expansion Procedure

High Energy Physics - Theory 2015-05-13 v1 Mathematical Physics math.MP

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".

Keywords

Cite

@article{arxiv.0903.4712,
  title  = {Dual Formulation of the Lie Algebra S-expansion Procedure},
  author = {Fernando Izaurieta and Alfredo Pérez and Eduardo Rodríguez and Patricio Salgado},
  journal= {arXiv preprint arXiv:0903.4712},
  year   = {2015}
}

Comments

12 pages, no figures