The dominance hierarchy in root systems of Coxeter groups.

DOI10.1016/j.jalgebra.2012.05.013zbMath1262.20042arXiv1108.2940OpenAlexW2080591607MaRDI QIDQ1939296

Xiang Fu

Publication date: 4 March 2013

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

Full work available at URL: https://arxiv.org/abs/1108.2940

zbMATH Keywords

algorithmsCoxeter groupsroot systemsdominanceelementary rootspositive rootsautomaticity

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Root systems (17B22)

Related Items (7)

Automata, reduced words and Garside shadows in Coxeter groups. ⋮ Small roots, low elements, and the weak order in Coxeter groups ⋮ \(n\)-low elements and maximal rank \(k\) reflection subgroups of Coxeter groups ⋮ Imaginary cones and limit roots of infinite Coxeter groups ⋮ NONORTHOGONAL GEOMETRIC REALIZATIONS OF COXETER GROUPS ⋮ Imaginary cone and reflection subgroups of Coxeter groups ⋮ Cone types, automata, and regular partitions in Coxeter groups

Cites Work

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• Reflection subgroups of Coxeter systems
• The conjugacy problem for Coxeter groups.
• The set of dominance-minimal roots
• A finiteness property and an automatic structure for Coxeter groups
• On outer automorphism groups of Coxeter groups
• Combinatorics of Coxeter Groups
• On the root system of a coxeter group

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