Abstract

A Jordan algebra is called special if it can be embedded in an associative algebra, and is called strongly special if its splittings by arbitrary bimodule extensions are special. The question of strong speciality of simple finite-dimensional Jordan algebras has been studied by N. Jacobson and K. McCrimmon (cf. [i, Chap. 7]). In this class, the only algebras which are not strongly special are the exceptional algebra H(C~ and the algebra of 6 × 6-matrices fixed with respect to a symmetric involution, as well as their forms.

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