Does there exist a classification of finite-dimensional Frobenius algebras in low dimensional cases. This question is motivated by the following analogous question for Hopf algebras.
$\begingroup$
$\endgroup$
4
asked Mar 30, 2023 at 16:54
-
4$\begingroup$ There are absolutely loads of them. I recently wrote a paper with Sambale about which small dimensional ones can be Morita equivalent to blocks of group algebras of finite groups, if that's of any help to you. $\endgroup$– Dave BensonCommented Mar 30, 2023 at 17:35
-
$\begingroup$ Since Frobenius algebras and Hopf algebras share a lot in common, why is that one of them (i.e. Hopg algebras) admit a classification in low dimensions but the other (Frobenius algebras) do not? $\endgroup$– Didier de MontblazonCommented Mar 31, 2023 at 10:27
-
2$\begingroup$ Can I suggest, by way of frustrating exercise, that you try to classify eight dimensional basic Frobenius algebras with one simple module? I think you may soon see why the definition is so much "floppier" and easier to satisfy than that of Hopf algebras. $\endgroup$– Dave BensonCommented Mar 31, 2023 at 15:09
-
1$\begingroup$ @DaveBenson: Ok - thanks for the suggestion! $\endgroup$– Didier de MontblazonCommented Mar 31, 2023 at 18:16
Add a comment
|