Cluster tilting modules for mesh algebras

We study cluster tilting modules in mesh algebras of Dynkin type as defined in [12], providing a new proof for their existence. Except for type G2, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain automorphism. We further study their mutation, p...

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Bibliographic Details
Published in:Linear algebra and its applications 2021-12, Vol.630, p.112-157
Main Authors: Erdmann, Karin, Gratz, Sira, Lamberti, Lisa
Format: Article
Language:English
Subjects:
Automorphisms
Cluster tilting modules
Clusters
Combinatorial analysis
Dynkin diagrams
Linear algebra
Mesh algebras
Modules
Mutation
Mutation of matrices
Mutation of modules
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Summary:We study cluster tilting modules in mesh algebras of Dynkin type as defined in [12], providing a new proof for their existence. Except for type G2, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain automorphism. We further study their mutation, providing an example of mutation in an abelian category which is not stably 2-Calabi-Yau, and explicitly describe the combinatorics.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.07.021