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arXiv · 2412.09552

Partial Hopf actions on generalized matrix algebras

Dirceu Bagio·Eliezer Batista·Hector Pinedo
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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 \cite{BP} for the existence of a unital partial action of $G$ on $R$.

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Dirceu Bagio, Eliezer Batista, Hector Pinedo. 2024-12-12. Partial Hopf actions on generalized matrix algebras. https://doi.org/10.1017/s0017089525100852

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