Actions of quantum linear spaces on quantum algebras

We study actions of bosonizations of quantum linear spaces on quantum algebras. Under mild conditions, we classify actions on quantum affine spaces and quantum matrix algebras. In the former case, it is shown that all actions of generalized Taft algebras are trivial extensions of actions on quantum...

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Bibliographic Details
Published inJournal of algebra Vol. 556; pp. 246 - 286
Main Authors Cline, Zachary, Gaddis, Jason
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.08.2020
Subjects
Hopf actions
Pointed Hopf algebras
Quantum algebras
Quantum linear spaces
Quantum algebras
16W50
Hopf actions
Quantum linear spaces
16W70
16T05
Pointed Hopf algebras
16S36
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ISSN0021-8693
1090-266X
DOI10.1016/j.jalgebra.2020.03.011

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Summary:We study actions of bosonizations of quantum linear spaces on quantum algebras. Under mild conditions, we classify actions on quantum affine spaces and quantum matrix algebras. In the former case, it is shown that all actions of generalized Taft algebras are trivial extensions of actions on quantum planes. In both cases we achieve bounds on the rank of the bosonization acting on the algebra.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2020.03.011