Partial Hopf actions on generalized matrix algebras

Let be a field, H a Hopf algebra over , and R = (ᵢMⱼ)1 ≤ i,j ≤ 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 = 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 .