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Towards a classification of simple partial comodules of Hopf algebras

par Batista, Eliezer;Hautekiet, William ;Saracco, Paolo ;Vercruysse, Joost
Référence Journal of algebra, 664, page (312-347)
Publication A Paraître, 2025-02-15

Article révisé par les pairs

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Résumé :

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.