Casimir operators induced by Maurer-Cartan equations
Abstract
It is shown that for inhomogeneous Lie algebras g=s( )L1 satisfying the condition N(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 R. The procedure is generalized to compute also the rational invariant of some Lie algebras.
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