Conjugacy classes and straight elements in Coxeter groups.

DOI10.1016/j.jalgebra.2014.03.008zbMath1300.20046arXiv1310.1021OpenAlexW2087308442MaRDI QIDQ402662

Timothée Marquis

Publication date: 28 August 2014

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

Full work available at URL: https://arxiv.org/abs/1310.1021

zbMATH Keywords

conjugacy classesCoxeter groupscyclically reduced wordsstraight elementsCoxeter elementsfully commutative elementsbraid relationscyclic shiftsDavis complexes

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Generators, relations, and presentations of groups (20F05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (4)

Scale and tidy subgroups for Weyl-transitive automorphism groups of buildings ⋮ Morphisms and order ideals of toric posets ⋮ Characterization of cyclically fully commutative elements in finite and affine Coxeter groups ⋮ Orthogonal forms of Kac-Moody groups are acylindrically hyperbolic.

Cites Work

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• On the cyclically fully commutative elements of Coxeter groups.
• Conjugacy of Coxeter elements.
• The conjugacy problem for Coxeter groups.
• Coxeter orbits and eigenspaces of Frobenius
• Minimal length elements in twisted conjugacy classes of finite Coxeter groups.
• Rank-one isometries of buildings and quasi-morphisms of Kac-Moody groups.
• Buildings
• Powers of Coxeter elements in infinite groups are reduced
• On the semisimplicity of polyhedral isometries

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