Grothendieck Group and Generalized Mutation Rule for 2-Calabi--Yau Triangulated Categories
By Yann Palu. 2008
65 citations recorded by the source corpus.
Abstract We compute the Grothendieck group of certain 2-Calabi–Yau triangulated categories appearing naturally in the study of the link between quiver representations and Fomin–Zelevinsky cluster algebras. In this setup, we also prove a generalization of the Fomin–Zelevinsky mutation rule.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/4458878d199357122625ae5a18fdce95e5d6edd4
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In Algebra and Number Theory
- Pierre-Guy Plamondon
- Vincent Pilaud
- Arnau Padrol
- Yann Palu
- B. Keller
- Lingyan Guo
- Thomas Brustle
- Dong Yang
In Geometry and Topology
- Pierre-Guy Plamondon
- Yann Palu
- Arnau Padrol
- Vincent Pilaud
- B. Keller
- Lingyan Guo
- Thomas Brustle
- Dong Yang
In Statistical and Nonlinear Physics
- Yann Palu
- Arnau Padrol
- Vincent Pilaud
- Pierre-Guy Plamondon
- B. Keller
- Lingyan Guo
- Thomas Brustle
- Dong Yang
Citations in the corpus
- Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors (2019, background): “Relations in the Grothendieck group of cluster categories have also been studied in [76].”
- Relative singularity categories I: Auslander resolutions (2012, unknown): “Palu [73] also obtained such an equivalence (in a slightly different form) in his study of Grothendieck groups of Calabi–Yau categories with cluster-tilting objects.”