Timeline for Hopf algebras vs. Kac algebras
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24 events
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| S Nov 10, 2022 at 15:08 | history | bounty ended | CommunityBot | ||
| S Nov 10, 2022 at 15:08 | history | notice removed | CommunityBot | ||
| Nov 9, 2022 at 15:20 | vote | accept | dm82424 | ||
| Nov 9, 2022 at 15:19 | vote | accept | dm82424 | ||
| Nov 9, 2022 at 15:20 | |||||
| Nov 9, 2022 at 12:21 | answer | added | dm82424 | timeline score: 1 | |
| Nov 4, 2022 at 15:41 | comment | added | JP McCarthy | It might be worth emailing these authors if you really want to know the answer. | |
| Nov 4, 2022 at 15:39 | comment | added | dm82424 | Okey, I just wanted to check that I wasn't missing anything. I agree that it looks like 24 is the smallest dimension, where this seems to be open. I previously had a look at "Some advances about the existence of compact involutions in semisimple Hopf algebra" by Abella and "On the Semisolvability of Semisimple Hopf Algebras of Low Dimension" by Natale. In the latter, she gives a table on the classification of s.s. Hopf algebras. The smallest dimension where this open is 24. However, Kac algebras of dimension 24 have been classified. This dimension was the original motivation for my question. | |
| Nov 4, 2022 at 15:23 | comment | added | JP McCarthy | Apologies if the two references first given were not relevant: I had hoped they might have been. | |
| Nov 4, 2022 at 15:19 | comment | added | JP McCarthy | I think we can deduce from SOME ADVANCES ABOUT THE EXISTENCE OF COMPACT INVOLUTIONS IN SEMISIMPLE HOPF ALGEBRAS that the question is open. In this paper it is shown that for dimensions up to 23 semisimple and finite dimensional Hopf algebras are finite quantum groups and thus Kac algebras. The general problem is left open. | |
| Nov 4, 2022 at 14:45 | comment | added | dm82424 | Hi, thanks for the two references. Could you expand a bit more on how they are related to my question? | |
| Nov 4, 2022 at 8:33 | comment | added | JP McCarthy | Also Compact involutions of semisimple quantum groups. Czech. J. Phys., vol. 44 (1994) pp. 963-972. link.springer.com/article/10.1007/BF01690448 | |
| Nov 4, 2022 at 8:33 | comment | added | JP McCarthy | Anything here: The set of types of n-dimensional semisimple and cosemisimple Hopf algebras is finite, J. Algebra 193 (1997), 571–580. | |
| Nov 3, 2022 at 11:49 | history | edited | dm82424 |
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| S Nov 2, 2022 at 13:35 | history | bounty started | dm82424 | ||
| S Nov 2, 2022 at 13:35 | history | notice added | dm82424 | Authoritative reference needed | |
| Nov 2, 2022 at 11:24 | history | edited | dm82424 | CC BY-SA 4.0 |
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| S Oct 25, 2022 at 10:46 | review | First questions | |||
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| S Oct 25, 2022 at 10:46 | history | asked | dm82424 | CC BY-SA 4.0 |