Drinfeld twists for monoidal Hom-bialgebras

TL;DR

This paper introduces Drinfeld twists for monoidal Hom-bialgebras, demonstrating how they can generate new structures while preserving key properties like R-matrices and monoidal equivalence of categories.

Contribution

It defines Drinfeld twists in the context of monoidal Hom-bialgebras and shows how these twists produce new Hom-bialgebras with preserved R-matrices and monoidally isomorphic representation categories.

Findings

Construction of new Hom-bialgebras via Drinfeld twists

Preservation of R-matrices under twists

Representation categories remain monoidally isomorphic

Abstract

The aim of this paper is to define and study Drinfeld twists for monoidal Hom-bialgebras. We show that a new Hom-bialgebra could be constructed by changing the coproduct of a monoidal Hom-bialgebra via a Drinfeld twist, and this construction preserves $R$-matrixes if there exist one. Moreover, their representation categories are monoidal isomorphic.