MUTATION ALGEBRAS OF A NONASSOCIATIVE ALGEBRA

The mutation algebra A(p, q) of a nonassociative algebra A is known to be Lie-admissible, as soon as A is flexible and Lie-admissible and p and q are elements in A, satisfying certain conditions. In the present paper it is shown that the A-algebra (a not associative assosymmetric algebra), Lie-admissible by nature but not flexible, has the property that A(p, q) is Lie-admissible, even if p and q are arbitrarily chosen in A. Some relevant remarks about Vinberg algebras conclude the study.