1,183 reputation
1623
bio website iaz.uni-stuttgart.de/…
location Stuttgart
age 28
visits member for 3 years, 6 months
seen 16 hours ago
Post-Doc working in representation theory

Oct
21
comment Higher vector spaces
@ChrisSchommer-Pries Thanks for pointing out this mistake. Of course the category should be cocomplete, otherwise there is the question what compact should mean if you don't have coproducts. I don't know of a theorem describing what properties describe finite dimensional vector spaces (or more general finitely generated, finitely presented, or coherent modules over a ring).
Oct
21
revised Higher vector spaces
added the assumption of being cocomplete
Oct
18
comment Higher vector spaces
@Najib Idrissi Yes, I changed accordingly.
Oct
18
revised Higher vector spaces
added 18 characters in body
Oct
16
answered Higher vector spaces
Oct
16
comment Higher vector spaces
Yes, sure. I was mixing up the tensor products, sorry.
Oct
16
comment Higher vector spaces
One needs commutative or an $(A,B^{op})$-bimodule. Otherwise the tensor functor will go to left modules instead of right modules. The image should be described by using a $k$-linear version of Morita's theorem: There should exist a compact progenitor. What do you mean by fully faithful for a $2$-functor?
Jul
3
comment Is there a homological way to compute quiver presentations?
Oh, sorry again: It is the $m$-th tensor power on the right hand side. This you should take to have arbitrary large path lengths in your relations.
Jul
3
comment Is there a homological way to compute quiver presentations?
Oh, the two $m$'s have a different meaning, unfortunately. The $m$ on the right hand side is just the summation index. The $m$ on the left hand side is the $A_\infty$-multiplication. A reference is [Keller: A-infinity algebras in representation theory], in the slightly different context of graded algebras [Lu, Palmieri, Wu, Zhang: A-infinity structure on Ext-algebras], or specifically about (a generalisation of) acyclic quiver, [Koenig, Külshammer, Ovsienko: Quasi-hereditary algebras, exact Borel subalgebras, A-infinity categories and boxes], taking standards to be simples, and ignoring box
Jul
2
awarded  Curious
Jul
2
comment Is there a homological way to compute quiver presentations?
I think Dag Madsen is suggesting the homological approach of computing the $A_\infty$-structure of the $\operatorname{Ext}$-algebra of the simples. This gives the quiver and relations. The relations are given by the image of a map $Dm:D\operatorname{Ext}^2(S,S)\to \bigoplus (D\operatorname{Ext}^1(S,S))^m$, where $S$ is the direct sum of all the simples.
Jun
20
answered What non-categorical applications are there of homotopical algebra?
Jun
19
awarded  Yearling
Mar
31
comment Cycles in Quivers and Path Algebras
You say you can't find anything for n > 2. What would be an answer for n = 2?
Mar
14
comment Derived category of varieties and derived category of quiver algebras
Could you give examples for 2 or 3 do not give each other or 1? I'm mostly interested in 2 does not give 1.
Jan
30
awarded  Nice Question
Jan
30
comment How can classifying irreducible representations be a “wild” problem?
@S.Carnahan What he appearently showed is that "a nice description of the conjugacy classes would lead to a nice description of wild quivers" [Arias-Castro, Diaconis, Stanley: A super-class walk on upper-triangular matrices]
Jan
30
asked How can classifying irreducible representations be a “wild” problem?
Sep
30
awarded  Caucus
Aug
21
reviewed Reviewed Partial (or complete) flag varieties as GIT quotients of affine spaces