On involutions of type \O(\q,k) over a field of\n characteristic two

2019/03/23 by Mark Hunnell, Hunnell, Mark, John Hutchens +3
Mathematics · #20G15 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1903.09904

openalex publication_date 2019/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study the involutions of \O(V,\q), an\northogonal group for a vector space V with quadratic form \q over a\nfield of characteristic 2. The classification proceeds by discussing conjugacy\nclasses of involutions arising as a product of transvections, involutions with\nrespect to a hyperbolic space, and involutions acting nontrivially in the\nradical of V. We achieve a complete classification of the conjugacy classes\nof involutions when the quadratic space (V,\q) is non-defective, and\nconclude with a discussion of the defective case.\n

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• Orthogonal involutions on central simple algebras and function fields of Severi-Brauer varieties