Related papers: Cycle-finite module categories
We describe the representation theory of finitely generated indecomposable modules over artin algebras which do not lie on cycles of indecomposable modules involving homomorphisms from the infinite Jacobson radical of the module category.
We solve a long standing open problem concerning the structure of finite cycles in the category mod A of finitely generated modules over an arbitrary artin algebra A, that is, the chains of homomorphisms $M_0 \stackrel{f_1}{\rightarrow} M_1…
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.
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…
We describe the structure of finite dimensional selfinjective algebras over an arbitrary field without short cycles of indecomposable modules.
In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.
In this paper we use A-infinity modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A-infinity modules. These varieties carry an action of an algebraic…
If ${\cal D}$ is a definable category then it may contain no nonzero finitely presented modules but, by a result of Makkai, there is a $\varinjlim$-generating set of strictly ${\cal D}$-atomic modules. These modules share some key…
Assume $A$ is weakly symmetric, indecomposable, with radical cube zero and radical square non-zero. We show that such algebra of wild representation type does not have a non-projective module $M$ whose ext algebra is finite-dimensional.…
In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which…
Given a cycle module M with a ring structure we show that the cycle complex with coefficients in M of a smooth scheme of finite type over a field has a A-infinity algebra structure. In the case of Milnor K-theory this gives a homotopy model…
We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…
Given a finite dimensional algebra $A$ over an algebraically closed field we study the relationship between the powers of the radical of a morphism in the module category of the algebra $A$ and the induced morphism in the module category of…
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…
All finite dimensional Nichols algebras with diagonal type of connected finite dimensional Yetter-Drinfeld modules over finite cyclic group $\mathbb Z_n$ are found. It is proved that finite dimensional Nichols algebra over $\mathbb Z_2$ is…
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…
In this paper, we will provide constructions of D-module structures on the complex computing the periodic cyclic homology of a stable infinity-category defined over a scheme of characteristic zero. We give two methods. The first one is…
Let $k$ be an algebraically closed field of characteristic $p\ge 0$. Let $G$ be an affine group scheme over $k$. We classify the indecomposable exact module categories over the rigid tensor category $\text{Coh}_f(G)$ of coherent sheaves of…
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…
We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…