On involutive cluster automorphisms
| Autor: | Ndouné Ndouné |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Group (mathematics) Quiver Mathematics::Rings and Algebras Automorphism Translation (geometry) Cluster algebra Combinatorics Mutation (knot theory) Affine space FOS: Mathematics Embedding Representation Theory (math.RT) Mathematics::Representation Theory Mathematics - Representation Theory Mathematics |
| Popis: | We construct a special embedding of the translation quiver $\mathbb{Z}Q$ in the three-dimensional affine space $\mathbb{R}^{3}$ where $Q$ is a finite connected acyclic quiver and $\mathbb{Z}Q$ contains a local slice whose quiver is isomorphic to the opposite quiver $Q^{op}$ of $Q.$ Via this embedding, we show that there exists an involutive anti-automorphism of the translation quiver $\mathbb{Z}Q.$ As an immediate consequence, we characterize explicitly the group of cluster automorphisms of the cluster algebras of seed $(X,Q)$, where $Q$ and $Q^{op}$ are mutation equivalent. 16 pages, 1 figure. arXiv admin note: text overlap with arXiv:1009.0742 by other authors |
| Databáze: | OpenAIRE |
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