Partial Hopf actions on generalized matrix algebras

Abstract Let $\Bbbk$ be a field, $H$ a Hopf algebra over $\Bbbk$ , and $R = (_iM_j)_{1 \leq i,j \leq n}$ 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 $H = \Bbbk G$ is the group algebra of a group $G$ , we recover the conditions given in [7] for the existence of a unital partial action of $G$ on $R$ .