Related papers: Classification of modules for infinite-dimensional…

Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…

Let $\Lambda$ be an artin algebra. We are going to consider full subcategories of $\mod\Lambda$ closed under finite direct sums and under submodules with infinitely many isomorphism classes of indecomposable modules. The main result asserts…

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known…

Let $\Lambda$ be an artin algebra. We obtain that $\Lambda$ is syzygy-finite when the radical layer length of $\Lambda$ is at most two; as two consequences, we give a new upper bound for the dimension of the bounded derived category of the…

Degeneration of modules is usually defined geometrically, but due to results of Zwara and Riedtmann we can also define it in terms of exact sequences. This definition also works over fields that are not algebraically closed. Let $k$ be a…

We find for each simple finitary Lie algebra $\mathfrak{g}$ a category $\mathbb{T}_\mathfrak{g}$ of integrable modules in which the tensor product of copies of the natural and conatural modules are injective. The objects in…

Irreducible nonzero level modules with finite-dimensional weight spaces are studied for non-twisted affine Lie superalgebras. A complete classification is obtained for superalgebras A(m,n)^ and C(n)^. In other cases the classification…

Since the introduction of Askey-Wilson algebras by Zhedanov in 1991, the classification of the finite-dimensional irreducible modules of Askey-Wilson algebras remains open. A universal analog $\triangle_q$ of the Askey-Wilson algebras was…

We use folding techniques to define a new class of gentle-like algebras that generalise the iterated tilted algebras of type $C$ and $\widetilde{C}$, which we call folded gentle algebras. We then show that folded gentle algebras satisfy…

The module category of any artin algebra is filtered by the powers of its radical, thus defining an associated graded category. As an extension of the degree of irreducible morphisms, this text introduces the degree of morphisms in the…

It is well known that if G is a finite group then the group of endotrivial modules is finitely generated. In this paper we prove that for an arbitrary finite group scheme G, and for any fixed integer n > 0, there are only finitely many…

Let $X$ be a finitely generated left module over a left artinian ring $R$, and let $p(X)=\{l_i\}$ be the infinite sequence of nonnegative integers where $l_i$ is the length of the $i$-th term of the minimal projective resolution of $X$. We…

It was conjectured at the end of the book "Representation theory of Artin algebras" by M. Auslander, I. Reiten and S. Smalo that an Artin algebra with the property that its finitely generated indecomposable modules are up to isomorphism…

In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.

We classify the simple infinite dimensional integrable modules with finite dimensional weight spaces over the quantized enveloping algebra of an untwisted affine algebra. We prove that these are either highest (lowest) weight integrable…

This article begins the study of irreducible maps involving finite-dimensional uniserial modules over finite-dimensional associative algebras. We work on the classification of irreducible maps between two uniserials over triangular…

Over fields of characteristic zero, we determine all absolutely irreducible Yetter-Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided…

In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…

The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…

This article concerns commutative algebras over a field $k$ of characteristic zero which are finite dimensional as vectorspaces, and particularly those of such algebras which are graded. Here the term graded is applied to non-negatively…