Factoring Euclidean isometries

DOI10.1142/S0218196715400135zbMath1315.51013arXiv1312.7780MaRDI QIDQ5246513

Noel Brady, Jon McCammond

Publication date: 21 April 2015

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.7780

zbMATH Keywords

intervalslatticesDedekind-MacNeille completionEuclidean isometriesreflection factorizations

Mathematics Subject Classification ID

Partial orders, general (06A06) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Complete lattices, completions (06B23) Euclidean geometries (general) and generalizations (51M05)

Related Items (13)

Decomposition of Garside groups and self-similar \(L\)-algebras ⋮ Factoring isometries of quadratic spaces into reflections ⋮ Reflection length in the general linear and affine groups ⋮ Artin groups of Euclidean type ⋮ Interval groups related to finite Coxeter groups. I ⋮ Reflection factorizations and quasi-Coxeter elements ⋮ Braid Groups and Euclidean Simplices ⋮ Proof of the \(K(\pi,1)\) conjecture for affine Artin groups ⋮ Computing reflection length in an affine Coxeter group ⋮ Projective metric geometry and Clifford algebras ⋮ Computing reflection length in an affine Coxeter group ⋮ Euclidean Artin-Tits groups are acylindrically hyperbolic ⋮ Dual Euclidean Artin groups and the failure of the lattice property.

Cites Work

• Braids, posets and orthoschemes
• A PARTIAL ORDER ON THE ORTHOGONAL GROUP
• On the conjugacy classes in the unitary, symplectic and orthogonal groups

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