1. Octonion Algebras over Rings Are Not Determined by their Norms
- Author
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Philippe Gille, Département de Mathématiques et Applications - ENS Paris (DMA), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Class (set theory) ,Ring (mathematics) ,Pure mathematics ,Algèbres d'octonions ,14L24, 20G41 ,Mathematics::Number Theory ,General Mathematics ,[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA] ,010102 general mathematics ,descente ,Mathematics - Rings and Algebras ,010103 numerical & computational mathematics ,01 natural sciences ,Octonion ,torseurs ,Rings and Algebras (math.RA) ,FOS: Mathematics ,Mathematics::Differential Geometry ,0101 mathematics ,Descent (mathematics) ,Mathematics - Abstract
Answering a question of H. Petersson, we provide a class of examples of pair of octonion algebras over a ring having isometric norms., Comment: 8 pages
- Published
- 2014
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