English

Casimir operators induced by Maurer-Cartan equations

High Energy Physics - Theory 2008-11-26 v2

Abstract

It is shown that for inhomogeneous Lie algebras g=sΛ(dimΛ)L1\frak{g}=\frak{s}\overrightarrow{\oplus}_{\Lambda}(\dim \Lambda)L_{1} satisfying the condition N(g)=1\mathcal{N}(\frak{g})=1, the only Casimir operator can be explicitly constructed from the Maurer-Cartan equations by means of wedge products. It is shown that this constraint imposes sharp bounds for the dimension of the representation RR. The procedure is generalized to compute also the rational invariant of some Lie algebras.

Keywords

Cite

@article{arxiv.0805.2982,
  title  = {Casimir operators induced by Maurer-Cartan equations},
  author = {R. Campoamor-Stursberg},
  journal= {arXiv preprint arXiv:0805.2982},
  year   = {2008}
}