Matched Pairs of Generalized Lie Algebras and Cocycle Twists

TL;DR

This paper introduces matched pairs of generalized Lie algebras and demonstrates that cocycle twists preserve the matched pair structure, advancing the understanding of algebraic deformations.

Contribution

It defines matched pairs of $(H, eta)$-Lie algebras and proves that cocycle twists maintain the matched pair property, providing new tools for algebraic construction.

Findings

Construction of $(H, eta)$-Lie algebras from matched pairs

Proof that cocycle twists of matched pairs are also matched

Enhanced understanding of algebraic deformations and twists

Abstract

We introduce the conception of matched pairs of $(H, \beta)$-Lie algebras, construct an $(H, \beta)$-Lie algebra through them. We prove that the cocycle twist of a matched pair of $(H, \beta)$-Lie algebras can also be matched.