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arXiv · 1008.2723

Special identities for quasi-Jordan algebras

Murray R. Bremner·Luiz A. Peresi
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Abstract

Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities $a(bc) = a(cb)$, $(ba)a^2 = (ba^2)a$, and $(b,a^2,c) = 2(b,a,c)a$. These identities are satisfied by the product $ab = a \dashv b + b \vdash a$ in an associative dialgebra. We use computer algebra to show that every identity for this product in degree $\le 7$ is a consequence of the three identities in degree $\le 4$, but that six new identities exist in degree 8. Some but not all of these new identities are noncommutative preimages of the Glennie identity.

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BibTeXRIS

Murray R. Bremner, Luiz A. Peresi. 2010-08-16. Special identities for quasi-Jordan algebras. https://arxiv.org/abs/1008.2723

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