Higher-order simple Lie algebras
High Energy Physics - Theory
2009-10-30 v3 dg-ga
Differential Geometry
Quantum Algebra
q-alg
Abstract
It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order `structure constants') which characterise the Lie algebra cocycles. This analysis allows us to present a classification of the higher-order simple Lie algebras as well as a constructive procedure for them. Our results are synthesised by the introduction of a single, complete BRST operator associated with each simple algebra.
Cite
@article{arxiv.hep-th/9605213,
title = {Higher-order simple Lie algebras},
author = {J. A. de Azcarraga and J. C. Perez Bueno},
journal= {arXiv preprint arXiv:hep-th/9605213},
year = {2009}
}
Comments
20 pages. Plain latex file. Minor changes. To appear in Commun. Math. Phys