Higher polynomial identities for mutations of associative algebras

Abstract

We study polynomial identities satisfied by the mutation product $xpy-yqx$ on the underlying vector space of an associative algebra $A$, where $p,q$ are fixed elements of $A$. We simplify known results for identities in degree $4$, proving that only two identities are necessary and sufficient to generate them all; in degree 5, we show that adding one new identity suffices; in degree 6, we demonstrate the existence of a number of new identities.

12 pages, 3 figures. The new version has a new coauthor and some improvements

References in corpus (1)

• Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions