On the Cohomology of Lie Algebras with an Invariant Inner Product

Abstract

In this work we consider the moduli space of all noncommutative metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over \(\mathbb C\) and \(\mathbb R\) up to dimension 5 and all metric Lie algebras over \(\mathbb C\) in dimension 6. We introduce cyclic and reduced cyclic cohomology to identify their metric deformations.