Involutions and stable subalgebras

JOURNAL OF ALGEBRA

卷:493

Article

Becher, Karim Johannes^1,2  Grenier-Boley, Nicolas³  Tignol, Jean-Pierre^1,4 

[1] Univ Konstanz, Zukunftskolleg FB Math & Stat, D-78457 Constance, Germany

[2] Univ Antwerp, Dept Wiskunde Informat, Middelheimlaan 1, B-2020 Antwerp, Belgium

[3] Univ Rouen Normandie, Univ Paris Diderot, Univ Cergy Pontoise, Univ Artois,Univ Paris Est Creteil,LDAR,EA 4434, F-76130 Mont St Aignan, France

[4] Catholic Univ Louvain, ICTEAM Inst, Ave G Lemaitre 4,Box L4-05-01, B-1348 Louvain La Neuve, Belgium

关键词: Central simple algebra;    Double Centraliser Theorem;    Maximal etale subalgebra;    Capacity;    Jordan algebra;    Crossed product;    Characteristic two;   

DOI  :  10.1016/j.jalgebra.2017.09.026

来源: Elsevier

【 摘 要 】

Given a central simple algebra with, involution over an arbitrary field, stable 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. (C) 2017 Elsevier Inc. A ll rights reserved.

【 授权许可】

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