Special Identity for Novikov–Jordan Algebras

2005

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DOI 10.1081/agb-200060504
Data confidence 70 medium
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Abstract

A commutative algebra with the identity (a * b) * (c * d) − (a * d) * (c * b) = (a, b, c) * d − (a, d, c) * b is called Novikov–Jordan. Example: K[x] under multiplication a * b = ∂(ab) is Novikov–Jordan. A special identity for Novikov–Jordan algebras of degree 5 is constructed. Free Novikov–Jordan algebras with q generators are exceptional for any q ≥ 1.