Cobraided Smash Product Hom-Hopf Algebras

TL;DR

This paper introduces a new class of Hom-Hopf algebras called R-smash products and provides conditions for these to be cobraided Hom-Hopf algebras, expanding the algebraic framework.

Contribution

It constructs R-smash product Hom-Hopf algebras and characterizes when they are cobraided, offering a novel algebraic structure and conditions.

Findings

Defined R-smash product Hom-Hopf algebras

Established necessary and sufficient conditions for cobraided structure

Expanded the theory of Hom-Hopf algebra constructions

Abstract

Let $(A,\a)$ and $(B,\b)$ be two Hom-Hopf algebras. In this paper, we construct a class of new Hom-Hopf algebras: $R$-smash product $(A\natural_R B,\a\o \b)$. Moreover, necessary and sufficient conditions for $(A\natural_R B,\a\o \b)$ to be a cobraided Hom-Hopf algebra are given.