Julian Kuelshammer
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 Aug 31 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 $Ext$-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 Oct 18 comment Higher vector spaces @Najib Idrissi Yes, I changed accordingly.