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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 …

Question: What are current open conjectures about the representation theory of the symmetric group? I am interested mostly in the characteristic 0 case, but conjectures for the modular case can also …

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 …

Finite connected partially ordered sets are in bijective correspondence to connected finite topological spaces that satisfy T_0, see for example the Wikipedia article Finite topological space. Here co …

$\DeclareMathOperator\Ext{Ext}\DeclareMathOperator\Hom{Hom}$>Question: What are some (open) homological conjectures that are also relevent for finite dimensional commutative algebras over a field $K$? …

Question: Is there an up to date summary of results on the classification of semisimple Hopf algebras over $\mathbb{C}$ (or a field of characteristic 0)? Here are some questions I wonder about: Que …

Let $A_n$ be the coinvariant algebra of the symmetric group $S_n$. This algebra has vector space dimension $n!$. $A_n$ is the quotient algebra of the polynomial ring $K[x_1,...,x_n]$ by the elementary …

The finitistic dimension of a finite dimensional algebra is defined as the supremum of all projective dimensions of modules having finite projective dimension. The finitistic dimension conjecture says …

Let $A$ be a a two-sided noetherian semiperfect ring and assume that the injective dimension of the left and right regular modules are equal to $n \geq 1$. Let $\Omega^n(mod A)$ be the category of $n$ …

Question 1:Is there a reference that lists all possible finite subgroups and their orders of $\mathrm{SO}(n)$ and $\mathrm{O}(n)$ for $n=4$ or even higher $n$ over the real numbers? I can only find …

Let $A$ be a noetherian ring (not necessarily commutative) or for simplicity even a finite dimensional algebra over a field. Let $X$ and $U$ be finitely generated $A$-modules and let $add(U)$ be the s …

It is well known that every representation-finite group algebra $KG$ is stable equivalent to a symmetric Nakayama algebra. Question: Is it true that every representation-finite Hopf algebra is stable …

Let $L$ be a finite lattice and $A=KL$ the incidence algebra of $L$. It should be true that $L$ is modular if and only if the algebra $KL$ is quadratic (since being modular is equivalent to having no …

Let $A=KQ$ be a path algebra of a connected quiver. (K algebraically closed if it helps) Question: Is there an explicit classification of all indecomposable $A$-modules $M$ that are rigid, that is $E …

Let $X$ be the poset of positive roots of a finite root system of Dynkin type $Q$. Question 1: In Dynkin type $A_n$, is it true that the poset of order ideals of $X$ is isomorphic to the poset of [2, …