Non-semisimple Lie algebras with Levi factor so(3), sl(2,R) and their invariants
Abstract
We analyze the number N of functionally independent generalized Casimir invariants for non-semisimple Lie algebras s% oplusRr with Levi factors isomorphic to so(3) and sl(2,R) in dependence of the pair (R,r) formed by a representation R of s and a solvable Lie algebra r. We show that for any dimension n >= 6 there exist Lie algebras sRr with non-trivial Levi decomposition such that N(s% oplusRr) = 0.
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