English
Related papers

Related papers: Modules over cluster-tilted algebras that do not l…

200 papers

We investigate weight modules for finite and infinite Weyl algebras, classifying all such simple modules. We also study the representation type of the blocks of locally-finite weight module categories and describe indecomposable modules in…

Rings and Algebras · Mathematics 2007-05-23 Viktor Bekkert , Georgia Benkart , Vyacheslav Futorny

We give an example of a cluster-tilted algebra A with quiver Q, such that the associated cluster algebra has a denominator vector which is not the dimension vector of any indecomposable A-module. This answers a question posed by T.…

Representation Theory · Mathematics 2020-12-21 Bethany Marsh , Idun Reiten

In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi-Yau tilted. With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so…

Representation Theory · Mathematics 2016-06-06 Ibrahim Assem , Ralf Schiffler , Khrystyna Serhiyenko

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…

Rings and Algebras · Mathematics 2019-10-31 Juan Orendain

For a given cluster-tilted algebra $A$ of tame type, it is proved that different indecomposable $\tau$-rigid $A$-modules have different dimension vectors. This is motivated by Fomin-Zelevinsky's denominator conjecture for cluster algebras.…

Rings and Algebras · Mathematics 2024-02-15 Changjian Fu , Shengfei Geng

Let $A$ be a hereditary algebra over an algebraically closed field $k$ and $A^{(m)}$ be the $m$-replicated algebra of $A$. Given an $A^{(m)}$-module $T$, we denote by $\delta (T)$ the number of non isomorphic indecomposable summands of $T$.…

Representation Theory · Mathematics 2013-01-24 Shunhua Zhang

In this paper we study the category of graded modules for the current algebra associated to $\mathfrak{sl}_2$. The category enjoys many nice properties, including a tilting theory which was established in previous work of the authors. We…

Representation Theory · Mathematics 2015-04-02 Matthew Bennett , Vyjayanthi Chari

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.

Representation Theory · Mathematics 2019-05-14 Piotr Malicki , Andrzej Skowroński

We show that if a graded submodule of a Noetherian module cannot be written as a proper intersection of graded submodules, then it cannot be written as a proper intersection of submodules at all. More generally, we show that a natural…

Commutative Algebra · Mathematics 2016-10-03 Justin Chen , Youngsu Kim

In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked surfaces. Based on this, we establish a bijection between tagged permissible curves and certain…

Representation Theory · Mathematics 2023-04-05 Ping He , Yu Zhou , Bin Zhu

In this paper, we show that the tilting modules over a cluster-tilted algebra $A$ lift to tilting objects in the associated cluster category $\mathcal{C}_H$. As a first application, we describe the induced exchange relation for tilting…

Representation Theory · Mathematics 2007-10-25 David Smith

In this paper we study a class of modules over infinite-dimensional Lie (super)algebras, which we call conformal modules. In particular we classify and construct explicitly all irreducible conformal modules over the Virasoro and the N=1…

q-alg · Mathematics 2009-09-25 Shun-Jen Cheng , Victor Kac

Let G be a semisimple, simply-connected algebraic group over an algebraically closed field of characteristic p > 0. We observe that the tensor product of the Steinberg module with a minuscule module is always indecomposable tilting.…

Representation Theory · Mathematics 2009-09-14 S. R. Doty

In this paper, we first construct the twisted full toroidal Lie algebra by an extension of a centreless Lie torus $LT$ which is a multiloop algebra twisted by several automorphisms of finite order and equipped with a particular grading. We…

Representation Theory · Mathematics 2021-03-22 Souvik Pal , S. Eswara Rao

We provide a classification of generalized tilting modules and full exceptional sequences for the dual extension algebra of the path algebra of a uniformly oriented linear quiver modulo the ideal generated by paths of length two with its…

Representation Theory · Mathematics 2022-04-01 Elin Persson Westin , Markus Thuresson

We describe the structure of module categories of finite dimensional algebras over an algebraically closed field for which the cycles of nonzero nonisomorphisms between indecomposable finite dimensional modules are finite (do not belong to…

Representation Theory · Mathematics 2013-10-24 Piotr Malicki , José A. de la Peña , Andrzej Skowroński

We construct a representation of the blob algebra over a ring allowing base change to every interesting (i.e. non--semisimple) specialisation which, in quasihereditary specialisations, passes to a full tilting module.

Representation Theory · Mathematics 2007-05-23 P P Martin , S Ryom-Hansen

We give a classification of infinite dimensional indecomposable weight modules over the Lie superalgebra $sl(2/1)$.

Quantum Algebra · Mathematics 2007-05-23 Yucai Su

We classify 1-tilting classes over an arbitrary commutative ring. As a consequence, we classify all resolving subcategories of finitely presented modules of projective dimension at most 1. Both these collections are in 1-1 correspondence…

Commutative Algebra · Mathematics 2016-06-06 Michal Hrbek

In the present paper the notion of a Hilbert module over a locally C*-algebra is discussed and some results are obtained on this matter. In particular, we give a detailed proof of the known result that the set of adjointable endomorphisms…

Operator Algebras · Mathematics 2007-05-23 Yu. I. Zhuraev , F. Sharipov