New answers tagged modules
2
votes
What is known about finite dimensional modules over the nilCoxeter algebra?
Motivated by the answers I tried to check when it is symmetric and I got the result that it symmetric is if and only if conjugation by the longest element acts as the identity in the corresponding ...
- 26.1k
3
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What is known about finite dimensional modules over the nilCoxeter algebra?
@DaveBenson, has already given a beautiful answer to this question. I just wanted to point out that a number of the things he says (although not his full computation of the dimension of the Ext-...
- 37.4k
10
votes
Accepted
What is known about finite dimensional modules over the nilCoxeter algebra?
This algebra has just one isomorphism class of simple module - let's call it $S$. Its projective cover is the regular representation, and is also the injective hull. The socle of the regular ...
- 11.8k
10
votes
Accepted
Factoring through projective modules is an equivalence relation
This equivalence relation is just a quotient of abelian groups. It will be cleaner to show that the $\mathrm{PHom}_R(M, N)$ is a subgroup of $\mathrm{Hom}_R(M,N).$ Indeed, if $f:M\to P_1 \to N$, $g: ...
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4
votes
Accepted
Monoidal structure on presheaves
The issue is that the diagonal functor $\mathcal C\to\mathcal C\otimes\mathcal C$ is not additive for a small pre-additive $\infty$-category $\mathcal C$ (and you want to take $\mathcal C=BR$), to ...
- 2,003
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