Involutions and stable subalgebras

Karim Johannes Becher (1, 2) , Nicolas Grenier-Boley (3) , Jean-Pierre Tignol (4)

1 Universität Konstanz
2 Universiteit Antwerpen = University of Antwerpen [Antwerpen]
3 LDAR (EA_4434) - Laboratoire de Didactique André Revuz
4 Département de mathématique [Louvain]

Given a central simple algebra with involution over an arbitrary field, étale 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.

Mots clés: Central simple algebra; Double Centraliser Theorem; maximaímaximaí etale subalgebra; capacity; Jordan algebra; crossed product; characteristic two

Domaines: Mathématiques [math]

Karim Johannes Becher, Nicolas Grenier-Boley, Jean-Pierre Tignol. Involutions and stable subalgebras. Journal of Algebra, 2018, 493, pp.381-409. ⟨10.1016/j.jalgebra.2017.09.026⟩. ⟨hal-01720483⟩