A comment concerning cohomology and invariants of Lie algebras with respect to contractions and deformations

Abstract

Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint module. A criterion to decide whether a given deformation is invertible or not is given in dependence of the Poincaré polynomial.

13 pages, 1 table

Cited by in corpus (2)

• Twisted cocycles of Lie algebras and corresponding invariant functions
• Contractions and deformations of quasi-classical Lie algebras preserving a non-degenerate quadratic Casimir operator