Related papers: Representation embeddings and the second Brauer-Th…

We start with observing that the only connected finite dimensional algebras with finitely many isomorphism classes of indecomposable bimodules are the quotients of the path algebras of uniformly oriented $A_n$-quivers modulo the radical…

The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…

We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in…

For a finite-dimensional gentle algebra, it is already known that the functorially finite torsion classes of its category of finite-dimensional modules can be classified using a combinatorial interpretation, called maximal non-crossing sets…

We consider the question of whether the injective modules generate the unbounded derived category of a ring as a triangulated category with arbitrary coproducts. We give an example of a non-Noetherian commutative ring where they don't, but…

We study the problem of classification of simple transitive 2-representations for the (non-finitary) 2-category of bimodules over the dual numbers. We show that simple transitive 2-representations with finitary apex are necessarily of rank…

In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories, a type of monoidal category equipped with a weak, not necessarily rigid duality. In combination…

Let $G$ be a finite group, $H$ be a normal subgroup of prime index $p$. Let $F$ be a field of either characteristic $0$ or prime to $|G|$. Let $\eta$ be an irreducible $F$-representation of $H$. If $F$ is an algebraically closed field of…

We study the construction of premonoidal categories, where the pentagon relation fails, through representations of finite group algebras and their quantum doubles. Both finite group algebras and their quantum doubles have a finite number of…

The representation dimension of an artin algebra as introduced by M.Auslander in his Queen Mary Notes is the minimal possible global dimension of the endomorphism ring of a generator-cogenerator. The paper is based on two texts written in…

The main goal of this paper is to study the class of algebras for which the global dimension of the endomorphism ring of the generator-cogenerator, given by the sum of the projective and injective modules, is equal to three. We will refer…

Let $\Lambda$ be an Auslander's 1-Gorenstein Artinian algebra with global dimension two. If $\Lambda$ admits a trivial maximal 1-orthogonal subcategory of $\mod\Lambda$, then for any indecomposable module $M \in \mod \Lambda$, we have that…

We prove that a finite braided tensor category A is invertible in the Morita 4-category BrTens of braided tensor categories if, and only if, it is non-degenerate. This includes the case of semisimple modular tensor categories, but also…

In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…

Given $n\leq d<\infty$, we investigate the existence of algebras of global dimension $d$ which admit an $n$-cluster tilting subcategory. We construct many such examples using representation-directed algebras. First, given two…

We begin the study of the representation theory of the infinite Temperley-Lieb algebra. We fully classify its finite dimensional representations, then introduce infinite link state representations and classify when they are irreducible or…

We determine the smallest irreducible Brauer characters for finite quasi-simple orthogonal type groups in non-defining characteristic. Under some restrictions on the characteristic we also prove a gap result showing that the next larger…

We determine the representation-finiteness of $A\otimes B$, where both $A$ and $B$ are simply connected algebras with at least three simple modules.

We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…

By a result of Orlov there always exists an embedding of the derived category of a finite-dimensional algebra of finite global dimension into the derived category of a high-dimensional smooth projective variety. In this article we give some…