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bio website iaz.uni-stuttgart.de/…
location Stuttgart
age 29
visits member for 4 years, 2 months
seen 7 hours ago
Post-Doc working in representation theory

1d
accepted $Ext$-algebra generated by $Hom$ and $Ext^1$ as $A_\infty$-algebra?
Aug
29
comment $Ext$-algebra generated by $Hom$ and $Ext^1$ as $A_\infty$-algebra?
@DagOskarMadsen Unfortunately, I was not able to find Keller's proof. In the cited paper it is only stated without proof. The only proof I could find is in [Conner: $A_\infty$-structures, generalized Koszul properties and combinatorial topology]. And this doesn't seem to generalise to other modules. For standard modules over quasi-hereditary algebras, Vanessa and I have an alternative proof. Do you have a reference or a sketch of Keller's proof?
Aug
28
comment Prove $R$ is a finite ring
This math.stackexchange question seems very related, in particular the comments on the accepted answer: math.stackexchange.com/q/289794/15416
Aug
28
comment $Ext$-algebra generated by $Hom$ and $Ext^1$ as $A_\infty$-algebra?
@MarianoSuárez-Alvarez That sounds more interesting. Do you have a reference for that?
Aug
28
comment $Ext$-algebra generated by $Hom$ and $Ext^1$ as $A_\infty$-algebra?
@MarianoSuárez-Alvarez Yes, you are right. But for Koszul modules, you also need only the algebra structure, not the $A_\infty$-structure, so it is quite restrictive. I want to know whether there are any other classes, where (at least sometimes) you need the $A_\infty$-structure as well.
Aug
28
comment $Ext$-algebra generated by $Hom$ and $Ext^1$ as $A_\infty$-algebra?
@JeremyRickard Thanks, I should have thought about that before posting. An example is obviously $k[1\to 2\to 3]/(ab)$. and $M=S(1)\oplus S(3)$.
Aug
28
revised $Ext$-algebra generated by $Hom$ and $Ext^1$ as $A_\infty$-algebra?
added 70 characters in body
Aug
28
asked $Ext$-algebra generated by $Hom$ and $Ext^1$ as $A_\infty$-algebra?
Jun
19
awarded  Yearling
Apr
7
comment Why is the A6 preprojective algebra of wild representation type?
There is a proof in [Erdmann-Skowronski: The stable Calabi-Yau dimension of tame symmetric algebras, Lemma 3.5 and Theorem 3.7]
Apr
2
comment The Jacobson radical of an infinite dimensional algebra
There is a general statement on the Jacobson radical of the path algebra of a quiver (without relations), see this mathoverflow question.
Apr
2
comment Why Jacobson, but not the left (right) maximals individually?
This statement is also proved in a slightly greater generality in [Coelho, Liu: Generalized path algebras. Interactions between ring theory and representations of algebras (Murcia), 53–66, Lecture Notes in Pure and Appl. Math., 210, Dekker, New York, 2000. MR1758401].
Mar
25
comment References for the bicategory of ring-bimodule pairs
@PavelSafronov That's a nice observation. If I understand it correctly from the brief look I took at the definition it should be a lax slice $2$-category over $\mathbb{Z}$ (resp. $k$).
Mar
25
asked References for the bicategory of ring-bimodule pairs
Mar
16
answered Kaplansky's 6th conjecture: dim(Irrep) | dim(algebra) - for semi-simple Hopf algebras
Mar
16
comment Kaplansky's 6th conjecture: dim(Irrep) | dim(algebra) - for semi-simple Hopf algebras
Probably clear to most readers, but this is false in positive characteristic. A counterexample is $\operatorname{SL}(2,p)$ with $p$ odd as explained in Curtis-Reiner, (17.17).
Mar
14
awarded  Popular Question
Feb
20
awarded  Electorate
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