Timeline for Low dimensional noncommutative non-cocommutative Hopf algebras
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| May 14, 2021 at 21:50 | history | edited | Konstantinos Kanakoglou | CC BY-SA 4.0 |
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| May 14, 2021 at 7:22 | vote | accept | Quin Appleby | ||
| May 13, 2021 at 23:38 | answer | added | Konstantinos Kanakoglou | timeline score: 9 | |
| May 11, 2021 at 13:40 | comment | added | მამუკა ჯიბლაძე | A Survey of Hopf Algebras of Low Dimension (Margaret Beattie, Acta Applicanda Mathematicæ 2009) is behind a paywall. On finite-dimensional Hopf algebras and their classifications (M. J. Hilgemann, Thesis, 2010) is free. | |
| May 11, 2021 at 12:46 | history | edited | Quin Appleby | CC BY-SA 4.0 |
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| May 11, 2021 at 12:18 | comment | added | Konstantinos Kanakoglou | More generally,it can be shown that all f.d. commutative hopf algebras over an algebraic closed field of char zero are duals to group hopf algebras. See: mathoverflow.net/q/257846/85967. So, if you exclude duals to group hopf algebras, anything else should be noncommutative. So, i think one can easily create a long list here (including taft algebras, quantum groups etc). | |
| May 11, 2021 at 12:09 | comment | added | Konstantinos Kanakoglou | The group algebra of a non-abelian group is non-commutative (and yet cocommutative). | |
| May 11, 2021 at 12:05 | answer | added | Calvin McPhail-Snyder | timeline score: 4 | |
| May 11, 2021 at 11:58 | comment | added | Quin Appleby | But these are commutative Hopf algebras? I am looking for noncommutative, not non-cocommutative. | |
| May 11, 2021 at 11:52 | comment | added | Konstantinos Kanakoglou | Basically, the way the question is posed, any group hopf algebra of a non-abelian group of suitable order would do. For example, regarding your lowest dimension i.e. $6$, take the group hopf algebra of the dihedral group $D_6\cong S_3$. | |
| May 11, 2021 at 11:30 | comment | added | Quin Appleby | Dimsnsion of the vector space. | |
| May 11, 2021 at 11:26 | comment | added | Qfwfq | By "dimension" is it meant the dimension of $A$ as a vector space over the base field, or the dimension of the corresponding "quantum group" (if the latter makes sense..)? | |
| May 11, 2021 at 11:17 | history | edited | Quin Appleby | CC BY-SA 4.0 |
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| May 11, 2021 at 11:00 | comment | added | JP McCarthy | When I Google 'hopf algebra dimension five' the first three hits are useful. | |
| May 11, 2021 at 10:37 | history | asked | Quin Appleby | CC BY-SA 4.0 |