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Given a Dynkin quiver $Q$ and a field $K$. Question 1: For which such $Q$ are there only finitely many indecomposable representations over the dual numbers $K[x]/(x^2)$? Note that those represen …

Assume $A$ is a finite dimensional quiver algebra such that two indecomposable modules are isomorphic iff their dimension vectors are equal. It is known that $A$ is in this case representation-finite …

Assume that the Schur algebra $S(n,r)$ with $n \geq r$ is not representation-finite. Question: For which $n$, $r$ is the quiver and relations of the blocks of $S(n, r)$ explicitly known? I just foun …

Let $A$ be a finite dimensional algebra . Let $P_{\inf}$ be the full subcategory of modules having finite projective dimension and $P_r$ the subcategory of modules having projective dimension bounded …

Question: Is there a classification of (noetherian if needed) integral domains with finitely many units ? (of course we can exclude fields as trivial examples) Probably there are many such domains t …

Given a quiver algebra A such that its trivial extension T(A) is representation-finite. Is T(A) automatically stable equivalent to a trivial extension algebra of a hereditary representation-finite alg …

Question 1:Is it true that the selfinjective (finite dimensional over an algebraically closed field K) algebras $A$ such that the stable module category of $A$ is 2-Calabi-Yau are exactly the deforme …

Let $A$ be a finite dimensional $K$-algebra over a field $K$ that is hereditary and of finite representation type. It is well known that they are classified by Dynkin diagrams. For algebraically close …

The Cartan matrix $C$ of a finite quiver algebra $A$ with points $e_i$ is defined as the matrix having entries $c_{i,j}=\dim(e_i A e_j)$. The Cartan determinant is defined as the determinant of the Ca …

Let $A$ be an Artin algebra and $C$ a subcategory of mod-$A$ that contains all projective modules and is closed under finite direct sums (but not necessarily under direct summands). Let $T:=add(C)$. …

A finite sequence $a_i$ is called logconvace in case $a_i^2 \geq a_{i-1} a_{i+1}$. Question : For a fixed $n$, is the sequence $a_{n,k}$ giving the number of Dyck paths of semilength $n$ having he …

Question: Are there known classes $X$ of finite dimensional algebras in the literature that have the property that in case $A, B \in X$ are derived equivalent, they share the same global dimension? …

Let $A$ be a finite dimensional quiver algebra such that two indecomposable modules are isomorphic iff their dimension vectors are the same. Let $T_A$ be the tits unit form of $A$ and $r_A$ the set of …

Let $A$ be an Artin algebra with enveloping algebra $A^e$. Then we have $Hom_{A^e}(X,A^e) \cong Hom_A(D(A) \otimes_A X,A)$ for a bimodule $X$. (see for example in the article "A theorem of Green on th …

Let $A$ be an Artin algebra and $M$ a module with $Ext^i(M,A)=0$ for $i=1,...,n-2$. Then in case $P_{n-1} \rightarrow ... \rightarrow P_0 \rightarrow M \rightarrow 0$ is the beginning of a minimal pro …