Year: 2025
Type: article
Abstract: Let double struck k k $\Bbbk$ be a field, upper H H $H$ a Hopf algebra over double struck k k $\Bbbk$ , and upper R equals left parenthesis Subscript i Baseline upper M Subscript j Baseline right parenthesis Subscript 1 less than or equals i comma j less than or equals n Baseline R = ( i M j ) 1 ≤ i , j ≤ n $R = (_iM_j)_{1 \leq i,j \leq n}$ a generalized matrix algebra. In this work, we establish necessary and sufficient conditions for upper H H $H$ to act partially on upper R R $R$ . 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 upper H equals double struck k upper G H = k G $H = \Bbbk G$ is the group algebra of a group upper G G $G$ , we recover the conditions given in [7] for the existence of a unital partial action of
Source: Glasgow Mathematical Journal
Authors: Dirceu Bagio, Eliezer Batista, Hector Pinedo
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416728119