Involutions and stable subalgebras - Becher, Karim Johannes; Grenier-Boley, Nicolas; Tignol, Jean-Pierre (My University, 2018)
Given a central simple algebra with involution over an arbitrary field, \'etale subalgebras contained in the space of symmetric elements are investigated. The method emphasizes the similarities between the various types of involutions and privileges a unified treatment for all characteristics whenever possible. As a consequence a conceptual proof of a theorem of Rowen is obtained, which asserts that every division algebra of exponent two and degree eight contains a maximal subfield that is a triquadratic extension of the centre.
Keywords: Central simple algebra, Double Centraliser Theorem, Maximal étale subalgebra, Capacity, Jordan algebra, Crossed product, Characteristic two; 510; 16H05; 16R50; 16W10