Coxeter elements and periodic Auslander-Reiten quiver.

DOI10.1016/j.jalgebra.2009.11.024zbMath1231.20035arXivmath/0703361OpenAlexW2013368745MaRDI QIDQ965150

J. Thind, Alexander A. jun. Kirillov

Publication date: 21 April 2010

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703361

zbMATH Keywords

Auslander-Reiten quiversroot systemsquiver representationsfinite Weyl groupsrepresentations of quiversCoxeter elementssimple reflectionssimply-laced Dynkin diagrams

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Representations of quivers and partially ordered sets (16G20) Root systems (17B22)

Related Items

Homological approach to the Hernandez-Leclerc construction and quiver varieties, Quantum McKay correspondence and global dimensions for fusion and module-categories associated with Lie groups, Polypositroids, Monoidal categorification and quantum affine algebras. II, Antisymmetric characters and Fourier duality, Cluster algebras of finite type via Coxeter elements and principal minors., Coxeter elements and root bases

Cites Work

• The enumeration of Coxeter elements
• On commutation classes of reduced words in Weyl groups
• Module categories, weak Hopf algebras and modular invariants
• Auslander-Reiten quivers and the Coxeter complex.
• Regular elements of finite reflection groups
• On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
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