On the Weak Order of Orthogonal Groups

DOI10.1080/00927872.2012.751991zbMATH Open1297.20041arXiv1110.4424OpenAlexW2190168428MaRDI QIDQ5412053

Annette Pilkington

Publication date: 25 April 2014

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

Abstract: A structure of a complete lattice (in the sense of a poset) is defined on the underlying set of the orhtogonal group of a real Euclidean space, by a construction analogous to that of the weak order of a Coxeter system in terms of its root system. This gives rise to a complte rootoid in the sense of Dyer, with the orthogonal group as underlying group.

Full work available at URL: https://arxiv.org/abs/1110.4424

zbMATH Keywords

convex conesorthogonal groupslatticesgroupoidsweak order

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Complete lattices, completions (06B23) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05) Root systems (17B22)

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