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We study the module categories of a tilted algebra C and the corresponding cluster-tilted algebra B. We investigate how various properties of a C-module are affected when considered in the module category of B. We give a complete…

Representation Theory · Mathematics 2019-10-16 Stephen Zito

We give the first example of a non-trivial cluster tilting module in a local finite dimensional algebra. To do this, we give an explicit calculation of the corresponding higher Auslander algebra by quiver and relations using the GAP-package…

Representation Theory · Mathematics 2025-05-20 Rene Marczinzik , Daniel Owens

In this paper we classify the irreducible integrable modules for the twisted toroidal extended affine Lie algebras with center acting non-trivially.

Representation Theory · Mathematics 2020-05-20 S. Eswara Rao , Sachin S. Sharma , Punita Batra

Tilting modules over commutative rings were recently classified in [12]: they correspond bijectively to faithful Gabriel topologies of finite type. In this note we extend this classification by dropping faithfulness. The counterpart of an…

Representation Theory · Mathematics 2016-02-16 Lidia Angeleri Hügel , Michal Hrbek

We are going to determine all the self-injective cluster tilted algebras. All are of finite representation type and special biserial.

Representation Theory · Mathematics 2007-05-29 Claus Michael Ringel

We study cluster tilting modules in mesh algebras of Dynkin type, providing a new proof for their existence. In all but one case, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain…

Representation Theory · Mathematics 2020-07-03 Karin Erdmann , Sira Gratz , Lisa Lamberti

We study thick subcategories defined by modules of complexity one in $\underline{\md}R$, where $R$ is the exterior algebra in $n+1$ indeterminates.

Representation Theory · Mathematics 2019-04-04 Otto Kerner , Dan Zacharia

The cluster-tilted algebras have been introduced by Buan, Marsh and Reiten, they are the endomorphism rings of cluster-tilting objects $T$ in cluster categories; we call such an algebra cluster-concealed in case $T$ is obtained from a…

Representation Theory · Mathematics 2009-12-31 Claus Michael Ringel

In this paper, we consider the twisted Hamiltonian extended affine Lie algebra (THEALA). We classify the irreducible integrable modules for these Lie algebras with finite-dimensional weight spaces when the finite-dimensional center acts…

Representation Theory · Mathematics 2024-05-07 Santanu Tantubay , Priyanshu Chakraborty , Punita Batra

In this note, we consider the $d$-cluster-tilted algebras, the endomorphism algebras of $d$-cluster-tilting objects in $d$-cluster categories. We show that a tilting module over such an algebra lifts to a $d$-cluster-tilting object in this…

Representation Theory · Mathematics 2008-12-29 Pin Liu

We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra…

Logic · Mathematics 2024-12-23 Lorna Gregory

The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type $A_n$, by counting the mutation class of any quiver with underlying graph $A_n$. It will also follow that if $T$ and…

Representation Theory · Mathematics 2008-04-16 Hermund André Torkildsen

We give a complete description of finitely generated modules over artin algebras which are not the middle of a short chain of modules, using injective and tilting modules over hereditary artin algebras.

Representation Theory · Mathematics 2013-12-13 Alicja Jaworska , Piotr Malicki , Andrzej Skowroński

An important result in tilting theory states that a class of modules over a ring is a tilting class if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective dimension. Moreover, cotilting classes are…

Representation Theory · Mathematics 2017-04-24 Frederik Marks , Jorge Vitória

In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…

Representation Theory · Mathematics 2025-06-05 Haibo Chen , Yucai Su , Yukun Xiao

We construct examples of bounded below, noncontractible, acyclic complexes of finitely generated projective modules over some rings $S$, as well as bounded above, noncontractible, acyclic complexes of injective modules. The rings $S$ are…

Rings and Algebras · Mathematics 2024-05-06 Leonid Positselski

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…

Rings and Algebras · Mathematics 2017-12-20 Yucai Su , Chunguang Xia , Lamei Yuan

The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…

Representation Theory · Mathematics 2007-05-23 Idun Reiten , Claus Michael Ringel

The paper is to classify irreducible integrable modules for the twisted full toroidal Lie algebra with some technical conditions. The twisted full toroidal Lie algebra are extensions of multiloop algebra twisted by sevaral finite order…

Representation Theory · Mathematics 2015-09-10 S. Eswara Rao , Punita Batra

Let $Q$ be a Dynkin quiver and $\Pi$ the corresponding set of positive roots. For the preprojective algebra $\Lambda$ associated to $Q$ we produce a rigid $\Lambda$-module $I_Q$ with $r=|\Pi|$ pairwise non-isomorphic indecomposable direct…

Representation Theory · Mathematics 2019-03-05 Christof Geiß , Bernard Leclerc , Jan Schröer