Representation dimension of quasi-tilted algebras

2010 ◽  
Vol 81 (2) ◽  
pp. 435-456 ◽  
Author(s):  
Steffen Oppermann
Keyword(s):  
Representation Dimension ◽  
Tilted Algebras

scholarly journals On representation dimension of tame cluster tilted algebras

2021 ◽  
Vol 39 (1) ◽  
pp. 107-132
Author(s):  
Alfredo Gonzalez Chaio ◽  
Sonia Trepode
Keyword(s):  
Representation Dimension ◽  
Tilted Algebras

The aim of this work is to study the representation dimension of cluster tilted algebras. We prove that the weak representation dimension of tame cluster tilted algebras is equal to three. We construct a generator module that reaches the weak representation dimension, unfortunately this module is not always a cogenerator. We show for which algebras this module gives the representation dimension.

Finite Repetitive Generalized Cluster Complexes and d-Cluster Categories

2013 ◽  
Vol 20 (01) ◽  
pp. 123-140
Author(s):  
Teng Zou ◽  
Bin Zhu
Keyword(s):  
Simplicial Complex ◽  
Root System ◽  
Cluster Complex ◽  
Cluster Complexes ◽  
Endomorphism Algebras ◽  
Tilted Algebras ◽  
Cluster Categories ◽  
Hereditary Algebras ◽  
Cluster Tilting ◽  
Tilting Objects

For any positive integer n, we construct an n-repetitive generalized cluster complex (a simplicial complex) associated with a given finite root system by defining a compatibility degree on the n-repetitive set of the colored root system. This simplicial complex includes Fomin-Reading's generalized cluster complex as a special case when n=1. We also introduce the intermediate coverings (called generalized d-cluster categories) of d-cluster categories of hereditary algebras, and study the d-cluster tilting objects and their endomorphism algebras in those categories. In particular, we show that the endomorphism algebras of d-cluster tilting objects in the generalized d-cluster categories provide the (finite) coverings of the corresponding (usual) d-cluster tilted algebras. Moreover, we prove that the generalized d-cluster categories of hereditary algebras of finite representation type provide a category model for the n-repetitive generalized cluster complexes.

scholarly journals AUSLANDER GENERATORS AND HOMOLOGICAL CONJECTURES

2013 ◽  
Vol 56 (3) ◽  
pp. 503-506 ◽  
Author(s):  
JIAQUN WEI
Keyword(s):  
Artin Algebra ◽  
Representation Dimension ◽  
Homological Conjectures

AbstractLet A be an artin algebra with representation dimension not more than 3. Assuming that AV is an Auslander generator and M ∈ addAV, we show that both findim(EndAM) and findim(EndAM)op are finite, and consequently the Gorenstein symmetry conjecture, the Wakamatsu-tilting conjecture and the generalized Nakayama conjecture hold for EndAM.

scholarly journals Maximal representation dimension of finitep-groups

2011 ◽  
pp. ---
Author(s):  
Shane Cernele ◽  
Masoud Kamgarpour ◽  
Zinovy Reichstein
Keyword(s):  
Representation Dimension ◽  
Maximal Representation

scholarly journals Tilted algebras

1982 ◽  
Vol 274 (2) ◽  
pp. 399-399 ◽  
Author(s):  
Dieter Happel ◽  
Claus Michael Ringel
Keyword(s):  
Tilted Algebras

scholarly journals Derived categories, tilted algebras, and Drinfel'd doubles

2003 ◽  
Vol 266 (2) ◽  
pp. 723-748 ◽  
Author(s):  
Liangang Peng ◽  
Youjun Tan
Keyword(s):  
Derived Categories ◽  
Tilted Algebras ◽  
Drinfel'd Doubles

scholarly journals Quasi-tilted algebras of canonical type

1996 ◽  
Vol 71 (2) ◽  
pp. 161-181 ◽  
Author(s):  
Helmut Lenzing ◽  
Andrzej Skowroński
Keyword(s):  
Tilted Algebras ◽  
Canonical Type
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