Special and exceptional Jordan dialgebras
Rings and Algebras
2011-05-16 v2 Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.1011.3683,
title = {Special and exceptional Jordan dialgebras},
author = {Vasily Voronin},
journal= {arXiv preprint arXiv:1011.3683},
year = {2011}
}
Comments
22 pages; added the statement about tetrads in Theorem 7, the criterion in Proposition 9, and the final remark