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Let $A_n$ be the Auslander algebra of $K[x]/(x^n)$. Is the representation dimension of $A_n$ known? For $n \leq 3$ the algebra is representation-finite and thus the representation dimension is 2. For …

With a friend I made a program in the GAP-package QPA to check whether a given finite dimensional quiver algebra is quasi-hereditary. It is very slow since it has to go through all permutations of poi …

Given a representation-finite finite dimensional algebra $A$ and an indecomposable module $M$. Question: What possible algebras can occur as $End_A(M)$? Note than when $End_A(M)$ is selfinjective, t …

Let $A$ be a finite dimensional algebra over a field $k$. A module $M$ is called exceptional in case $End_A(M)=k$ and $Ext_A^i(M,M)=0$ for $i>0$. A tuple $(M,N)$ is called exceptional in case $M$ and …

I asked here: Are all algebras igusa-todorov? wheter all algebras are Igusa-Todorov. There was given a counterexample using a certain selfinjective algebra. Since I made the answer green there I post …

Let $A$ be a selfinjective finite dimensional algebra and $M$ an indecomposable non-projective module. Let $N=A \oplus M$. Then a minimal right add(N)-approximation of a module is defined as a map $f: …

Let $A$ be a local algebra and $M$ an indecomposable $A$-modules. When is the algebra $B:=End_A(A \oplus M)$ standardly stratified? In particular, is $End_A(A \oplus S)$ standardly stratified for a si …

Recall that a finite dimensional quiver (always assume connected quiver) algebra is selfinjective iff $P(S) \rightarrow P(socP)$ is a permutation (called the nakayama permutation), when S is simple an …

Given a quiver algebra $A=kQ/I$ with underlying quiver $Q$ being a linear oriented Dynkin quiver of type $\mathcal{A}$. Such an algebra is uniquely determined by the sequence $[c_0,c_1,...,c_{n-1}]$ w …

(Algebras are assumed to be finite dimensional and connected over a field here) Over an algebraically closed field the classification of representation-finite symmetric algebras is very nice up to sta …

Given a representation-finite algebra $A$. Is there a quick method to find all modules $M$ with $End_A(M)=A$? Motivation is that those are the modules with a natural $A$-bimodule structure. We might a …

Let $A$ be a representation finite hereditary algebra. Define the Euler form by $f(M,N):=dim(Ext^1(M,N))-dim(Hom(M,N))$ for two modules $M,N$. Now if $A_1$ and $A_2$ are two representation-finite here …

Let $A$ be a finite dimensional connected algebra over a field and $X$ the set of all $A$-right modules $M$ with $End_A(M) \cong A$. Say $A$ has property $(*)$ in case the following is true: Given $ …

Can the finite representation-finite rings with at most 2 simple modules be classified? Is there a non-serial local representation-finite finite ring?

Let $X_n$ be the set of Nakayama algebras with a linear connected quiver and n simple modules. Define a relation on $X_n$ by saying that two such algebras are equivalent if one is isomorphic to the en …