Timeline for Hopf algebras arising as Group Algebras
Current License: CC BY-SA 2.5
19 events
| when toggle format | what | by | license | comment | |
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| May 4, 2022 at 21:03 | history | edited | Martin Sleziak |
added the tag (hopf-algebras)
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| Jan 7, 2018 at 16:56 | comment | added | Watson | Related: math.stackexchange.com/questions/2595567 | |
| Dec 17, 2009 at 13:56 | vote | accept | John McCarthy | ||
| Dec 17, 2009 at 5:53 | comment | added | Theo Johnson-Freyd | I'm with Ben. "Group algebra" definitely means the algebra of finite linear combinations of group elements; functions on the group is something else. The way to measure the difference is whether the corresponding functor to Algebras is co- or contravariant. | |
| Dec 16, 2009 at 16:05 | comment | added | Ben Webster♦ | Kevin- You'll note, I made no claims about whether what I wrote was true. But with "commutative" in it, that claim is quite false, whereas with "cocommutative" it's morally correct, if with a caveat or two. | |
| Dec 16, 2009 at 15:53 | history | edited | Greg Kuperberg |
edited tags
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| Dec 16, 2009 at 13:52 | answer | added | David E Speyer | timeline score: 14 | |
| Dec 16, 2009 at 9:44 | answer | added | Mark Hovey | timeline score: 2 | |
| Dec 16, 2009 at 1:31 | answer | added | Mariano Suárez-Álvarez | timeline score: 1 | |
| Dec 16, 2009 at 1:29 | comment | added | Greg Kuperberg | @Kevin: In context, John may have meant finite-dimensional Hopf algebras over $\mathbb{C}$. And I suspect that Ben was not tripped up by anything other than the abbreviated framing of the question. For one, the question's formalism is indeed dual to what I usually take to be a group algebra. | |
| Dec 16, 2009 at 0:43 | comment | added | Kevin McGerty | Ben it depends how you define the group algebra -- functions on the group is a perfectly good way to go. Also, as Greg mentions below, at least in positive characteristic this is false no? You would have to say finite group scheme, which is just a tautology really. | |
| Dec 16, 2009 at 0:22 | answer | added | Greg Kuperberg | timeline score: 7 | |
| Dec 15, 2009 at 23:54 | comment | added | Ben Webster♦ | Don't you mean "Every cocommutative finite dimensional Hopf algebra is the group algebra of some finite group."? | |
| Dec 15, 2009 at 23:54 | answer | added | Ben Webster♦ | timeline score: 7 | |
| Dec 15, 2009 at 23:27 | answer | added | darij grinberg | timeline score: 2 | |
| Dec 15, 2009 at 22:59 | history | edited | John McCarthy | CC BY-SA 2.5 |
added 2 characters in body
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| Dec 15, 2009 at 22:57 | comment | added | John McCarthy | Something a little more refined would be nice, but it's a good start. | |
| Dec 15, 2009 at 22:20 | comment | added | javier | One could say that having a basis consisting on group-like elements is precisely what you want, but I reckon you are after a more refined characterization... | |
| Dec 15, 2009 at 22:06 | history | asked | John McCarthy | CC BY-SA 2.5 |