Towards a classification of simple partial comodules of Hopf algebras

Making the first steps towards a classification of simple partial comodules, we give a general construction for partial comodules of a Hopf algebra H using central idempotents in right coideal subalgebras and show that any 1-dimensional partial comodule is of that form. We conjecture that in fact al...

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Bibliographic Details
Published in:Journal of algebra 2025-02, Vol.664, p.312-347
Main Authors: Batista, Eliezer, Hautekiet, William, Saracco, Paolo, Vercruysse, Joost
Format: Article
Language:English
Subjects:
Partial comodule
Partial corepresentation
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Summary:Making the first steps towards a classification of simple partial comodules, we give a general construction for partial comodules of a Hopf algebra H using central idempotents in right coideal subalgebras and show that any 1-dimensional partial comodule is of that form. We conjecture that in fact all finite-dimensional simple partial H-comodules arise this way. For H=kG for some finite group G, we give conditions for the constructed partial comodule to be simple, and we determine when two of them are isomorphic. If H=kG⁎, then our construction recovers the work of M. Dokuchaev and N. Zhukavets [12]. We also study the partial modules and comodules of the non-commutative non-cocommutative Kac-Paljutkin algebra A.
ISSN:0021-8693
DOI:10.1016/j.jalgebra.2024.10.005