bio  website  iaz.unistuttgart.de/… 

location  Stuttgart  
age  29  
visits  member for  4 years, 2 months 
seen  7 hours ago  
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PostDoc working in representation theory
1d

accepted  $Ext$algebra generated by $Hom$ and $Ext^1$ as $A_\infty$algebra? 
Aug
29 
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$Ext$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 quasihereditary algebras, Vanessa and I have an alternative proof. Do you have a reference or a sketch of Keller's proof? 
Aug
28 
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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 
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$Ext$algebra generated by $Hom$ and $Ext^1$ as $A_\infty$algebra?
@MarianoSuárezAlvarez That sounds more interesting. Do you have a reference for that? 
Aug
28 
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$Ext$algebra generated by $Hom$ and $Ext^1$ as $A_\infty$algebra?
@MarianoSuárezAlvarez 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 
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$Ext$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 
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Why is the A6 preprojective algebra of wild representation type?
There is a proof in [ErdmannSkowronski: The stable CalabiYau dimension of tame symmetric algebras, Lemma 3.5 and Theorem 3.7] 
Apr
2 
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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 
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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 
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References for the bicategory of ringbimodule 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 ringbimodule pairs 
Mar
16 
answered  Kaplansky's 6th conjecture: dim(Irrep)  dim(algebra)  for semisimple Hopf algebras 
Mar
16 
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Kaplansky's 6th conjecture: dim(Irrep)  dim(algebra)  for semisimple 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 CurtisReiner, (17.17). 
Mar
14 
awarded  Popular Question 
Feb
20 
awarded  Electorate 
Oct
21 
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Higher vector spaces
@ChrisSchommerPries 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 