Year: 2026
Type: preprint
Abstract: We study the theory of right representations of Novikov algebras. We introduce the notion of a modular right ideal of a Novikov algebra and prove that every irreducible right representation of a Novikov algebra is isomorphic to the quotient by a maximal modular right ideal. We prove that the class of Novikov algebras with no irreducible representations forms a hereditary radical. We introduce the notion of a primitive Novikov algebra and show that a Novikov algebra is primitive if and only if it admits an almost faithful irreducible representation. We also introduce the notion of the quasi-kernel of a representation, defined as the largest ideal contained in its kernel. Finally, we prove that the constructed radical coincides with the intersection of the quasi-kernels of all its irreducible representations.
Source: arXiv (Cornell University)
Author: Panasenko, A. S.
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164906863