Details

Autor(en) / Beteiligte

• Mira, José Antonio Cuenca

Titel

THIRD-POWER ASSOCIATIVE ABSOLUTE VALUED ALGEBRAS WITH A NONZERO IDEMPOTENT COMMUTING WITH ALL IDEMPOTENTS

Ist Teil von

• Publicacions matemàtiques, 2014-01, Vol.58 (2), p.469-484

Ort / Verlag

Universitat Autònoma de Barcelona

Erscheinungsjahr

2014

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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 $\mathop C\limits^* ,\mathop H\limits^* ,or\mathop {\rm O}\limits^* $, obtained from C, H, or O by imposing a new product denned 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.