Related papers: Cycle-finite modules over artin algebras

The class of finitely presented algebras over a field K with a set of generators a_1,...,a_n and defined by homogeneous relations of the form a_1a_2...a_n = a_{sigma(1)}a_{sigma(2)}...a_{sigma(n)}, where sigma runs through an abelian…

This paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalizes the critical groups of complex finite group representations studied by Benkart, Klivans, Reiner and Gaetz. A…

We construct all finite irreducible modules over Lie conformal superalgebras of type K

Existence of superdecomposable pure-injective modules reflects complexity in the category of finite-dimensional representations over an algebra. Such an existence occurs when an algebra is non-domestic; a conjecture due to M. Prest. G.…

In this paper, we study the tensor structure of category of finite dimensional representations of Drinfeld quantum doubles $D(H_n(q))$ of Taft Hopf algebras $H_n(q)$. Tensor product decomposition rules for all finite dimensional…

We complete the classification of the finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent elements in classical Lie algebras. This extends earlier work where this classification is…

In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.

Exact indecomposable module categories over the tensor category of representations of Hopf algebras that are liftings of quantum linear spaces are classified.

We classify fields having finitely many finite non-commutative (not necessarily central) division algebras over them. In the process, we introduce the notion of anti-closure of a field and also make comments on fields having a linear…

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…

An artin algebra $A$ is said to be CM-finite if there are only finitely many, up to isomorphisms, indecomposable finitely generated Gorenstein-projective $A$-modules. We prove that for a Gorenstein artin algebra, it is CM-finite if and only…

For the Kronecker algebra, Zwara found in [14] an example of a module whose orbit closure is neither unibranch nor Cohen-Macaulay. In this paper, we explain how to extend this example to all representation-infinite algebras with a…

We define a type B analogue of the category of finite sets with surjections, and we study the representation theory of this category. We show that the opposite category is quasi-Grobner, which implies that submodules of finitely generated…

Let $k$ be a field. We characterize the group schemes $G$ over $k$, not necessarily affine, such that $\mathsf{D}_{\mathrm{qc}}(B_kG)$ is compactly generated. We also describe the algebraic stacks that have finite cohomological dimension in…

We show that the moduli problem of deformations of nilpotent displays by quasi-isogenies is representable, without using $p$-divisible groups. The main ingredients are Artin's criterion and the theory of truncated displays. This gives in…

We classify finite irreducible conformal modules over a class of infinite Lie conformal algebras ${\frak {B}}(p)$ of Block type, where $p$ is a nonzero complex number. In particular, we obtain that a finite irreducible conformal module over…

Let $A$ be a finite dimensional symmetric Hopf algebra over a field $k$. We show that there are $A$-modules whose Tate cohomology is not finitely generated over the Tate cohomology ring of $A$. However, we also construct $A$-modules which…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

In the context of representation theory of finite dimensional algebras, string algebras have been extensively studied and most aspects of their representation theory are well-understood. One exception to this is the classification of…