Expanding Lie (Super)Algebras through Abelian Semigroups

We propose an outgrowth of the Expansion Method introduced by de Azcarraga, Izquierdo, Picon and Varela in [Nucl. Phys. B 662 (2003) 185]. The basic idea consists in considering the direct product between an abelian semigroup S and a Lie algebra g. General conditions under which relevant subalgebras can systematically be extracted from S \\otimes g are given. We show how, for a particular choice of semigroup S, the known cases of expanded algebras can be reobtained. Explicit examples, including the M Algebra and a D'Auria-Fre-like Superalgebra, are considered. Finally, we find explicit, non-trace invariant tensors for these S-expanded algebras, which are essential ingredients in e.g. the formulation of Supergravity theories in arbitrary space-time dimensions.

Перевод пока недоступен