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Partial Hopf actions on generalized matrix algebras
Part of:
Rings and algebras arising under various constructions
Hopf algebras, quantum groups and related topics
Published online by Cambridge University Press: 26 November 2025
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 
$R$.
MSC classification
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust
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