Reflection group presentations arising from cluster algebras

DOI10.1090/S0002-9947-2014-06147-3zbMath1444.20026arXiv1112.2300OpenAlexW1991627122WikidataQ59897627 ScholiaQ59897627MaRDI QIDQ5496652

Bethany R. Marsh, Michael Barot

Publication date: 2 February 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.2300

zbMATH Keywords

presentationdiagramWeyl groupcyclefinite typeCoxeter graphDynkin diagramreflection groupmutationcluster algebracompanion basisquasi-Cartan companion

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60) Root systems (17B22)

Related Items (16)

Braid groups and quiver mutation ⋮ Artin group presentations arising from cluster algebras ⋮ Interval groups related to finite Coxeter groups. I ⋮ Geometric description of \(C\)-vectors and real Lösungen ⋮ Isomorphism and non-isomorphism for interval groups of type \(D_n\) ⋮ Recovering the topology of surfaces from cluster algebras ⋮ On maximal green sequences for type \(\mathbb{A}\) quivers ⋮ EXPLICIT CONSTRUCTION OF COMPANION BASES ⋮ Cluster algebras from surfaces and extended affine Weyl groups ⋮ Companion bases for cluster-tilted algebras ⋮ Reflection group relations arising from cluster algebras ⋮ Coxeter groups, quiver mutations and geometric manifolds ⋮ A lattice isomorphism theorem for cluster groups of mutation-Dynkin type \(A_{n}\) ⋮ Cluster algebras and symmetric matrices ⋮ Quiver mutations and Boolean reflection monoids ⋮ Presentations of groups with even length relations

Cites Work

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• Cluster-concealed algebras.
• Companion bases for cluster-tilted algebras
• Generalized Serre relations for Lie algebras associated with positive unit forms
• Signed graphs, root lattices, and Coxeter groups
• Cluster algebras. II: Finite type classification
• Tilting theory and cluster combinatorics.
• Cluster algebras I: Foundations
• CLUSTER ALGEBRAS OF FINITE TYPE AND POSITIVE SYMMETRIZABLE MATRICES
• Quivers with relations arising from clusters (𝐴_{𝑛} case)

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