Timeline for Group representation with algebra structure
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 21, 2019 at 17:45 | comment | added | Student | Added! Thanks for the comment. At least point I'm not sure if I want those too. But since the picture comes from TQFT, I'd suppose to! My original intention was to get some pointers to useful references, but it hasn't been done yet, I should dig more into my question and make it more precise. | |
| Nov 21, 2019 at 17:41 | comment | added | მამუკა ჯიბლაძე | @Student Could you please add to the question what exactly do you mean by compatibility? For example, $\mathbb C[G]$ also has a right $G$-action and satisfies $(ab)g=a(bg)$ and $(ag)b=a(gb)$, do you want these too? | |
| Nov 21, 2019 at 17:38 | comment | added | Student | Hmm yes it is not natural. The instance in my mind comes from Witten-Dijkgraaf 2d-TQFT, where representations are assigned to points. It seems to me that the algebra structure of $\mathbb{C}[G]$ plays an important role.. so I'd like to know more examples.. or even a classification if any. | |
| Nov 21, 2019 at 16:33 | comment | added | Tom De Medts | Oh, I see, I should have looked at your example more carefully. (I also see now that you want associative unital algebras, which is also not what I had in mind.) I think that your definition of "compatible" is less natural (because the elements of $G$ do not induce automorphisms of this algebra structure), but of course your question makes perfect sense. | |
| Nov 21, 2019 at 14:33 | comment | added | Student | Hmm.. I did not mention explicitly, but as my example $\mathbb{C}[G]$ suggests, the algebra is compatible in the way that $g(ab) = (ga)b$. In your answer, I suppose you mean $Hom_G(V\otimes V,V)$. However, $G$ acts on $V\otimes V$ by $g(v\otimes w) = gv\otimes gw$. | |
| Nov 21, 2019 at 9:17 | history | answered | Tom De Medts | CC BY-SA 4.0 |