Partial Hopf actions on generalized matrix algebras

Abstract

Let $\mathbb{k}$ be a field, $H$ a Hopf algebra over $\mathbb{k}$, and $R={(}_i{M}_j{)}_{1\le i,j\le n}$ a generalized matrix algebra. In this work, we establish necessary and sufficient conditions for $H$ to act partially on $R$. To achieve this, we introduce the concept of an opposite covariant pair and demonstrate that it satisfies a universal property. In the special case where $H=\mathbb{k}G$ is the group algebra of a group $G$, we recover the conditions given in \cite{BP} for the existence of a unital partial action of $G$ on $R$.