Special and exceptional Jordan dialgebras

Details Special and exceptional Jordan dialgebras Special and exceptional Jordan dialgebras

2010-11-16

arxiv.org/abs/1011.3683v2

Mathematics

Rings and Algebras

22 pages; added the statement about tetrads in Theorem 7, the criterion in Proposition 9, and the final remark

Scientific paper

In this paper, we study the class of Jordan dialgebras. We develop an approach for reducing problems on dialgebras to the case of ordinary algebras. It is shown that straightforward generalizations of the classical Cohn's, Shirshov's, and Macdonald's Theorems do not hold for dialgebras. However, we prove dialgebraic analogues of these statements. Also, we study polylinear special identities which hold in all special Jordan algebras and do not hold in all Jordan algebras. We find a natural correspondence between special identities for ordinary algebras and dialgebras.

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