A generalization of Scheunert's Theorem on cocycle twisting of color Lie algebras

TL;DR

This paper extends Scheunert's classical theorem, demonstrating that the twisting of algebra structures and bicharacters via 2-cocycles for color Lie algebras is possible for any group, not just finitely generated abelian groups.

Contribution

It generalizes Scheunert's theorem to arbitrary groups, broadening the applicability of cocycle twisting in color Lie algebra theory.

Findings

Twisting of algebra structures by 2-cocycles is possible for any group.

Extension of the theorem from finitely generated abelian groups to all groups.

Broader framework for cocycle twisting in color Lie algebras.

Abstract

A classical theorem of Scheunert on $G$-color Lie algebras, asserts in the case of finitely generated abelian groups, one can twist the algebra structure and the commutation bicharacter on $G$ by a 2-cocycle twist to a super-Lie $G$ graded, algebra. In this paper we show that this can be done for an arbitrary group.