Timeline for Tannakian description of a semi-direct product
Current License: CC BY-SA 2.5
8 events
when toggle format | what | by | license | comment | |
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Jun 30, 2012 at 16:20 | vote | accept | AFK | ||
May 4, 2011 at 22:14 | vote | accept | AFK | ||
May 4, 2011 at 22:14 | |||||
May 14, 2010 at 15:47 | comment | added | Torsten Ekedahl | @David: Yes, the non-split case is a problem for the relative Tannakian which will no doubt result in me actually reading through your answer :-) | |
May 14, 2010 at 13:32 | comment | added | David Ben-Zvi | Torsten - thanks, that is more Tannakian! (I guess the description I gave should extend to nonsplit group extensions, but in the split case may be overkill) | |
May 14, 2010 at 4:18 | comment | added | Torsten Ekedahl | ... In this case the group scheme is just $K$ with the given action of $H$ (of course it may not be a finite group scheme so its affine algebra may not lie in $Rep_k(H)$ but rather in the category of ind-objects for $Rep_k(H)$. | |
May 14, 2010 at 4:18 | comment | added | Torsten Ekedahl | A more Tannakian answer along the same lines is relative Tannakian theory. Restriction to $H$ gives a fibre functor $Rep_k(G) \to Rep_k(H)$ and the surjection $G\to H$ gives a "constant object" functor $Rep_k(H) \to Rep_k(G)$. One can imitate the usual Tannaka theory replacing $Rep_k(1)=Vec_k$ by $Rep_k(H)$ getting a description of $Rep_k(G)$ as the category of modules in $Rep_k(H)$ of some group scheme in $Rep_k(H)$. .... | |
May 13, 2010 at 23:45 | history | edited | David Ben-Zvi | CC BY-SA 2.5 |
added 60 characters in body
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May 13, 2010 at 23:19 | history | answered | David Ben-Zvi | CC BY-SA 2.5 |