Abstract: Given a nonassociative algebra A with a derivation d, let us define its derived algebra as the same linear space A equipped with two operations of multiplication a<b = a d(b), a>b = d(a) b, for a,b in A. The purpose of this talk is to show how to derive the identities that hold on all such derived algebras provided that A ranges through a given variety of nonassociative algebras. (In particular, for the variety of associative and commutative algebras the result is very well known: the variety of Novikov algebras appears in this way.) We also study the natural embedding problem related to the functor transforming a differential algebra into its derived algebra. We state a sufficient condition that guarantees an affirmative answer to the embedding problem and show an example when the embedding problem has a negative solution.

Cite: Kolesnikov P.S.
Derived nonassociative algebras: identities and embedding problem
X Nonassociative Day Online 18-18 Dec 2023