Factoring isometries of quadratic spaces into reflections

DOI10.1016/j.jalgebra.2022.03.017OpenAlexW4221128565MaRDI QIDQ2142474

Giovanni Paolini, Jon McCammond

Publication date: 27 May 2022

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

Full work available at URL: https://arxiv.org/abs/2103.02507

zbMATH Keywords

orthogonal groupsquadratic spacesG E Wall's characterization of orthogonal grouppositive reflections, ordered fields

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Quadratic forms over general fields (11E04) Quadratic spaces; Clifford algebras (11E88)

Cites Work

• The structure of a unitary factor group
• Unipotent elements and the spinor norms of Wall and Zassenhaus
• Products of positive reflections in real orthogonal groups
• The generation of \(\text{Sp}(\mathbb F_2)\) by transvections
• Artin groups of Euclidean type
• Proof of the \(K(\pi,1)\) conjecture for affine Artin groups
• Dual Euclidean Artin groups and the failure of the lattice property.
• On the spinor norm
• Applications of the wall form to unipotent isometries of index two
• The dual braid monoid
• Products of Positive Reflections in the Orthogonal Group
• A PARTIAL ORDER ON THE ORTHOGONAL GROUP
• Factoring Euclidean isometries
• Non-crossing partition lattices in finite real reflection groups
• On the conjugacy classes in the unitary, symplectic and orthogonal groups
• On the Decomposition of Orthogonalities into Symmetries
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