Right representations of Novikov algebras

Abstract

We consider the concept of a right representation for Novikov algebras. We introduce the concept of a right modular ideal of a Novikov algebra and obtain a description of irreducible right representations of a Novikov algebra as quotients by maximal modular right ideals. We prove that the class of Novikov algebras without irreducible representations is a hereditary radical. We introduce the concept of a primitive Novikov algebra and prove that a Novikov algebra is primitive if and only if it has an almost faithful irreducible representation. We introduce the concept of the quasi-kernel of a representation as the largest ideal contained in the kernel of the representation. We prove that the Jacobson radical of a Novikov algebra is the intersection of the quasi-kernels of all irreducible representations of this algebra.