k-involutions of SL(n,k) over Fields of Characteristic 2

2015/09/30 by Nathaniel Schwartz, Schwartz, Nathaniel
Mathematics · #20CXX #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1510.00054

openalex publication_date 2015/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Symmetric k-varieties generalize Riemannian sym\-me\-tric spaces to reductive groups defined over arbitrary fields. For most perfect fields, it is known that symmetric k-varieties are in one-to-one correspondence with isomorphy classes of k-involutions. Therefore, it is useful to have representatives of each isomorphy class in order to describe the k-varieties. Here we give matrix representatives for each isomorphy class of k-involutions of SL(n,k) in the case that k is any field of characteristic 2; we also describe fixed point groups of each type of involution.

Related

• Isomorphy Classes of Involutions of SP(2n, k), n>2
• Isomorphy Classes of k-Involutions of SO(n, k,β), n > 2
• Isomorphism classes of k-involutions of algebraic groups of type E₆
• Involutions of reductive Lie algebras in positive characteristic
• Fixed point groups of involutions of type O(q,k) over a field of characteristic two