Mutation algebras of a nonassociative algebra
This paper contains some results on classes of Lie-admissible (nonassociative) algebras and their (left) \((p,q)\)-mutation algebras, defined by the altered product \(x \circ y : = (xp)y - (yq)x\). It is shown that every mutation of an assosymmetric algebra (defined by the property that the associator of any three elements is unchanged by permutations of these, yet not every associator is zero) is Lie-admissible. A weaker result is shown to hold for Vinberg algebras (also known as left-symmetric algebras): For every element \(r\) in the right nucleus of a Vinberg algebra, the \((r,r)\)-mutation is Lie-admissible.
scientific article; zbMATH DE number 816058
scientific article