On homotopes of Novikov algebras.

Abstract

Given a unital associative commutative ring Φ containing \(\frac{1}{2}\), we consider a homotope of a Novikov algebra, i.e., an algebra \(A_\varphi \) that is obtained from a Novikov algebra A by means of the derived operation \(x \cdot y = xy\varphi \) on the Φ-module A, where the mapping ϕ satisfies the equality \(xy\varphi = x(y\varphi )\). We find conditions for a homotope of a Novikov algebra to be again a Novikov algebra.