This article is cited in 6 papers

Differentiably simple Jordan algebras

A. A. Popov<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: We prove that each exceptional differentiably simple Jordan algebra over a field of characteristic 0 is an Albert ring whose elements satisfy a cubic equation with the coefficients in the center of the algebra. If the characteristic of the field is greater than 2 then such an algebra is the tensor product of its center and a central exceptional simple $27$-dimensional Jordan algebra. Some remarks made on special algebras.

Keywords: Jordan algebra, derivation, differentiably simple algebra.

UDC: 512.554.7

Received: 04.07.2012

 English version: Siberian Mathematical Journal, 2013, 54:4, 713–721

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