scholarly journals Construction of tilted algebras

1981 ◽  
pp. 125-144 ◽  
Author(s):  
Dieter Happel ◽  
Claus Michael Ringel
Keyword(s):  
Tilted Algebras

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 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 CHARACTERIZATION OF NAKAYAMA $m$-CLUSTER TILTED ALGEBRAS OF TYPE $A_n$

2017 ◽  
Vol 22 (2) ◽  
Author(s):  
Faisal Faisal ◽  
Intan Muchtadi-Alamsyah
Keyword(s):  
Tilted Algebras

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

scholarly journals Tame Quasi-tilted Algebras

1998 ◽  
Vol 203 (2) ◽  
pp. 470-490 ◽  
Author(s):  
Andrzej Skowroński
Keyword(s):  
Tilted Algebras

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.

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