Isomorphism classes of k-involutions of algebraic groups of type E₆

2015/04/17 by John Hutchens, Hutchens, John
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1504.04587

openalex publication_date 2015/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Automorphisms of order 2 are studied in order to understand generalized symmetric spaces. The groups of type E₆ we consider here can be realized as both the group of linear maps that leave a certain determinant invariant, and also as the identity component of the automorphism group of a class of structurable algebras known as Brown algebras. We will classify the k-involutions of these groups of type E₆ using aspects of both descriptions, and give detailed descriptions of representatives over certain fields including algebraically closed fields, ℝ, \mathbbF_p, and ℚ_p.

Related

• Isomorphy Classes of k-Involutions of SO(n, k,β), n > 2
• Isomorphy Classes of Involutions of SP(2n, k), n>2
• k-involutions of SL(n,k) over Fields of Characteristic 2
• Involutions of type G₂ over a field of characteristic 2
• On involutions and generalized symmetric spaces of dicyclic groups