Radicals of Lie-solvable Novikov algebras

TL;DR

This paper characterizes radicals in Lie-solvable Novikov algebras, showing their equivalence to specific sets of elements, and explores property stability under the Gelfand-Dorfman construction.

Contribution

It establishes the equivalence of Baer and right-nilpotent radicals, and Andrunakievich and largest left-quasiregular ideals in Lie-solvable Novikov algebras, and studies property stability post-Gelfand-Dorfman.

Findings

Baer radical equals all right-nilpotent elements

Andrunakievich radical equals largest left-quasiregular ideal

Property stability under Gelfand-Dorfman construction

Abstract

We prove that in a Lie-solvable Novikov algebra, the Baer radical coincides with the set of all right-nilpotent elements, and the Andrunakievich radical coincides with the largest left-quasiregular ideal. We investigate the stability of some properties of commutative algebras with derivation after applying the Gelfand-Dorfman construction.