scholarly journals On the Galois coverings of a cluster-tilted algebra

2009 ◽  
Vol 213 (7) ◽  
pp. 1450-1463 ◽  
Author(s):  
Ibrahim Assem ◽  
Thomas Brüstle ◽  
Ralf Schiffler
Keyword(s):  
Tilted Algebra ◽  
Galois Coverings ◽  
Cluster Tilted Algebra

Hochschild cohomology of m-cluster tilted algebras of type 𝔸̃

2020 ◽  
pp. 2150018
Author(s):  
Viviana Gubitosi
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Groups ◽  
Tilted Algebra ◽  
Type Formula ◽  
Tilted Algebras ◽  
Gerstenhaber Algebra ◽  
Cluster Tilted Algebra ◽  
Multiplicative Structures

In this paper, we compute the dimension of the Hochschild cohomology groups of any [Formula: see text]-cluster tilted algebra of type [Formula: see text]. Moreover, we give conditions on the bounded quiver of an [Formula: see text]-cluster tilted algebra [Formula: see text] of type [Formula: see text] such that the Gerstenhaber algebra [Formula: see text] has nontrivial multiplicative structures. We also show that the derived class of gentle [Formula: see text]-cluster tilted algebras is not always completely determined by the dimension of the Hochschild cohomology.

The Auslander–Reiten components of $\mathcal{K}^b({\rm proj}\, \Lambda)$ for a cluster-tilted algebra of type Ã

2014 ◽  
Vol 14 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Kristin Krogh Arnesen ◽  
Yvonne Grimeland
Keyword(s):  
Main Tool ◽  
Type A ◽  
Tilted Algebra ◽  
Cluster Tilted Algebra

We classify the Auslander–Reiten components of [Formula: see text], where Λ is a cluster-tilted algebra of type Ã. The main tool is the combinatoric description of the indecomposable complexes in [Formula: see text] via homotopy strings and homotopy bands.

scholarly journals THE FIRST HOCHSCHILD COHOMOLOGY GROUP OF A CLUSTER TILTED ALGEBRA REVISITED

2013 ◽  
Vol 23 (04) ◽  
pp. 729-744 ◽  
Author(s):  
IBRAHIM ASSEM ◽  
JUAN CARLOS BUSTAMANTE ◽  
KIYOSHI IGUSA ◽  
RALF SCHIFFLER
Keyword(s):  
Vector Space ◽  
Cohomology Group ◽  
Hochschild Cohomology ◽  
Tilted Algebra ◽  
Direct Sum ◽  
Hochschild Cohomology Group ◽  
Cluster Tilted Algebra

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH 1(B) with coefficients in the B–B-bimodule B. If C is a tilted algebra such that B is the relation extension of C by [Formula: see text], then we prove that HH 1(B) is isomorphic, as a vector space, to the direct sum of HH 1(C) with HH 1(B,E). This yields homological interpretations for results of the first and the fourth authors with M. J. Redondo.

scholarly journals τ-Tilting finite cluster-tilted algebras

2020 ◽  
Vol 63 (4) ◽  
pp. 950-955 ◽  
Author(s):  
Stephen Zito
Keyword(s):  
Tilted Algebra ◽  
Tilted Algebras ◽  
Cluster Tilted Algebra

We prove if B is a cluster-tilted algebra, then B is τB-tilting finite if and only if B is representation-finite.

scholarly journals Finding a cluster-tilting object for a representation finite cluster-tilted algebra

2010 ◽  
Vol 121 (2) ◽  
pp. 249-263 ◽  
Author(s):  
M. A. Bertani-Økland ◽  
S. Oppermann ◽  
A. Wrålsen
Keyword(s):  
Tilted Algebra ◽  
Cluster Tilting Object ◽  
Tilting Object ◽  
Cluster Tilting ◽  
Cluster Tilted Algebra

Open Frobenius Cluster-Tilted Algebras

2022 ◽  
Vol 29 (01) ◽  
pp. 1-22
Author(s):  
Viviana Gubitosi
Keyword(s):  
Finite Type ◽  
Tilted Algebra ◽  
Frobenius Structures ◽  
Tilted Algebras ◽  
Cluster Tilted Algebra

In this paper, we compute the Frobenius dimension of any cluster-tilted algebra of finite type. Moreover, we give conditions on the bound quiver of a cluster-tilted algebra [Formula: see text] such that [Formula: see text] has non-trivial open Frobenius structures.

scholarly journals THE ALGEBRAS DERIVED EQUIVALENT TO GENTLE CLUSTER TILTED ALGEBRAS

2012 ◽  
Vol 11 (01) ◽  
pp. 1250012 ◽  
Author(s):  
GRZEGORZ BOBIŃSKI ◽  
ASLAK BAKKE BUAN
Keyword(s):  
Tilted Algebra ◽  
Type Formula ◽  
Finite Dimensional ◽  
Tilted Algebras ◽  
Dynkin Type ◽  
Euclidean Type ◽  
Finite Dimensional Algebras ◽  
Cluster Tilted Algebra

A cluster tilted algebra is known to be gentle if and only if it is cluster tilted of Dynkin type 𝔸 or Euclidean type [Formula: see text]. We classify all finite-dimensional algebras which are derived equivalent to gentle cluster tilted algebras.

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