Novikov algebras and their primitive ideals

Abstract

The aim of this paper is to study the primitive ideals of Novikov algebras. In terms of modular maximal right ideals, a characterization of the primitive ideals of a Novikov algebra has been obtained. We prove a Chevalley-Jacobson density-type theorem for primitive Novikov algebras. We obtain some equivalences between prime, simple, and primitive Novikov algebras. We describe a subalgebra of a Novikov algebra as a Novikov algebra of endomorphisms.