Generic modules for tilted algebras

Xianneng Du

doi:10.1007/bf02882428

Generic modules for tilted algebras

Chinese Science Bulletin ◽

10.1007/bf02882428 ◽

1997 ◽

Vol 42 (3) ◽

pp. 177-180

Author(s):

Xianneng Du

Keyword(s):

Tilted Algebras ◽

Generic Modules

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Generic modules and tameness

Differential Tensor Algebras and their Module Categories ◽

10.1017/cbo9781139107105.032 ◽

2011 ◽

pp. 335-344

Author(s):

R. Bautista ◽

L. Salmeron ◽

R. Zuazua

Keyword(s):

Generic Modules

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Finite Repetitive Generalized Cluster Complexes and d-Cluster Categories

Algebra Colloquium ◽

10.1142/s1005386713000114 ◽

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.

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