Third-power associative absolute valued algebras with a nonzero idempotent commuting with all idempotents
Cuenca Mira, José Antonio (Universidad de Málaga. Departamento de Álgebra, Geometría y Topología)

Date:	2014
Abstract:	This paper deals with the determination of the absolute valued algebras with a nonzero idempotent commuting with the remaining idempotents and satisfying x2x = xx2 for every x. We prove that, in addition to the absolute valued algebras R, C, H, or O of the reals, complexes, division real quaternions or division real octonions, one such absolute valued algebra A can also be isometrically isomorphic to some of the absolute valued algebras C. H or O, obtained from C, H, and O by imposing a new product defined by multiplying the conjugates of the elements. In particular, every absolute valued algebra having the above properties is finite-dimensional. This generalizes some well known theorems of Albert, Urbanik and Wright, and El-Mallah.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Absolute valued algebra ; Idempotent ; Division algebra ; Third-power associativity ; Pairwise commuting elements
Published in:	Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 469-484, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287186
DOI: 10.5565/PUBLMAT_58214_23

16 p, 332.2 KB

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