Special identity for Novikov-Jordan algebras

摘要

A commutative algebra with the identity (a * b) * (c * d) - (a * d) * (c * b) = (a, b, c) * d - (a, d, e) * b is called Novikov-Jordan. Example: Kx under multiplication a * b = partial derivative(ab) is Novikor-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.