Hom-center-symmetric algebras and bialgebras

TL;DR

This paper introduces hom-center-symmetric algebras, explores their bimodules and duals, and establishes connections with hom-Lie algebras, culminating in a theorem linking these structures and their bialgebras.

Contribution

It constructs hom-center-symmetric algebras, defines their bimodules and duals, and links them to hom-Lie algebras and bialgebras, providing new theoretical insights.

Findings

Established relations between dual bimodules and matched pairs of hom-Lie algebras

Defined the Manin triple for hom-center-symmetric algebras

Proved a theorem linking matched pairs, bialgebras, and sub-adjacent hom-Lie algebras

Abstract

In this work, the hom-center-symmetric algebras are constructed and discussed. Their bimodules, dual bimodules and matched pairs are defined. The relation between the dual bimodules of hom-center-symmetric algebras and the matched pairs of hom-Lie algebras is established. Furthermore, the Manin triple of hom-center-symmetric algebras is given. Finally, a theorem linking the matched pairs of hom-center-symmetric algebras, the hom-center-symmetric bialgebras and the matched pairs of sub-adjacent hom-Lie algebras is provided.