Involutions and stable subalgebras

Becher, Karim Johannes;Grenier-Boley, Nicolas;Tignol, Jean-Pierre
(2018) Journal of Algebra — Vol. 493, n° 1, p. 381-409 (2018)

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Authors
  • Becher, Karim JohannesUniversiteit Antwerpen
    Author
  • Grenier-Boley, NicolasUniversité Rouen Normandie, Université Artois, Université Cergy-Pontoise, Université Paris Diderot, Université Paris Est Créteil
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  • Tignol, Jean-Pierreorcid-logoUCLouvain
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Abstract
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.
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Becher, K. J., Grenier-Boley, N., & Tignol, J.-P. (2018). Involutions and stable subalgebras. Journal of Algebra, 493(1), 381-409. https://doi.org/10.1016/j.jalgebra.2017.09.026 (Original work published 2018)