Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D

Janine Bastian; Thorsten Holm; Sefi Ladkani

doi:https://doi.org/10.1016/j.jalgebra.2014.03.034

Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D

Janine Bastian, Thorsten Holm, Sefi Ladkani

Research output: Contribution to journal › Article › peer-review

Abstract

We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle questions remain open. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmically more tractable, and give a complete classification together with standard forms.

Original language	American English
Pages (from-to)	277-332
Number of pages	56
Journal	Journal of Algebra
Volume	410
DOIs	https://doi.org/10.1016/j.jalgebra.2014.03.034
State	Published - 15 Jul 2014
Externally published	Yes

Keywords

Cartan determinant
Cartan matrix
Cluster tilted algebra
Cluster tilting object
Derived category
Derived equivalence
Dynkin diagram
Finite representation type
Good mutation
Quiver mutation
Tilting complex

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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https://doi.org/10.1016/j.jalgebra.2014.03.034

Cite this

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title = "Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D",

abstract = "We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle questions remain open. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmically more tractable, and give a complete classification together with standard forms.",

keywords = "Cartan determinant, Cartan matrix, Cluster tilted algebra, Cluster tilting object, Derived category, Derived equivalence, Dynkin diagram, Finite representation type, Good mutation, Quiver mutation, Tilting complex",

author = "Janine Bastian and Thorsten Holm and Sefi Ladkani",

note = "Funding Information: This work has been carried out in the framework of the research priority program SPP 1388 Representation Theory of the Deutsche Forschungsgemeinschaft (DFG). We gratefully acknowledge financial support through the grants HO 1880/4-1 and LA 2732/1-1. S. Ladkani was also supported by a European Postdoctoral Institute (EPDI) fellowship.",

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doi = "https://doi.org/10.1016/j.jalgebra.2014.03.034",

language = "American English",

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journal = "Journal of Algebra",

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T1 - Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D

AU - Bastian, Janine

AU - Holm, Thorsten

AU - Ladkani, Sefi

N1 - Funding Information: This work has been carried out in the framework of the research priority program SPP 1388 Representation Theory of the Deutsche Forschungsgemeinschaft (DFG). We gratefully acknowledge financial support through the grants HO 1880/4-1 and LA 2732/1-1. S. Ladkani was also supported by a European Postdoctoral Institute (EPDI) fellowship.

PY - 2014/7/15

Y1 - 2014/7/15

N2 - We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle questions remain open. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmically more tractable, and give a complete classification together with standard forms.

AB - We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle questions remain open. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmically more tractable, and give a complete classification together with standard forms.

KW - Cartan determinant

KW - Cartan matrix

KW - Cluster tilted algebra

KW - Cluster tilting object

KW - Derived category

KW - Derived equivalence

KW - Dynkin diagram

KW - Finite representation type

KW - Good mutation

KW - Quiver mutation

KW - Tilting complex

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M3 - Article

SN - 0021-8693

VL - 410

SP - 277

EP - 332

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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