Timeline for Given an algebra, can it be realized as a block of a Hopf algebra?
Current License: CC BY-SA 3.0
7 events
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| Sep 7, 2011 at 18:22 | history | bounty ended | Julian Kuelshammer | ||
| Sep 5, 2011 at 9:26 | comment | added | Julian Kuelshammer | Could you provide references for your arguments? Why is the Ext-algebra graded commutative if $B$ is not the principal block? Is it calculated somewhere in this particular example? | |
| Sep 2, 2011 at 19:51 | comment | added | Julian Kuelshammer | I haven't checked your argument about graded commutativity yet. Let me give the example, where to find, that $k[x,y]/x^2,y^2$ is the block of a Hopf algebra. In [Xiao: Finite dimensional representations of $U_t(sl(2))$ at roots of unity] the example $k[a,b]/a^2-b^2,ab$ is given, which is isomorphic to the above stated algebra via the isomorphism $a+ib\mapsto x, a-ib\mapsto y$. | |
| Sep 2, 2011 at 15:16 | comment | added | John Palmieri | If $B$ is a block, then shouldn't $Ext_B^*(k,k)$ be graded commutative? In the particular example you gave, it looks like that would force $q$ to be $-1$, not 1. But I may be completely misunderstanding... | |
| Aug 31, 2011 at 21:45 | history | edited | Julian Kuelshammer |
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| Aug 31, 2011 at 17:34 | history | bounty started | Julian Kuelshammer | ||
| Jun 20, 2011 at 10:43 | history | asked | Julian Kuelshammer | CC BY-SA 3.0 |