Quasi-Frobenius Novikov algebras and pre-Novikov bialgebras

TL;DR

This paper explores the structure of quasi-Frobenius Novikov algebras and their connection to pre-Novikov algebras, introducing new concepts like double constructions and the pre-Novikov Yang-Baxter equation to advance the theory of Novikov bialgebras.

Contribution

It establishes a natural pre-Novikov algebra structure for quasi-Frobenius Novikov algebras and introduces the pre-Novikov Yang-Baxter equation and double constructions, expanding the theoretical framework.

Findings

Characterization of double constructions via pre-Novikov bialgebras

Introduction of the pre-Novikov Yang-Baxter equation

Symmetric solutions produce pre-Novikov bialgebras

Abstract

Pre-Novikov algebras and quasi-Frobenius Novikov algebras naturally appear in the theory of Novikov bialgebras. In this paper, we show that there is a natural pre-Novikov algebra structure associated to a quasi-Frobenius Novikov algebra. Then we introduce the definition of double constructions of quasi-Frobenius Novikov algebras associated to two pre-Novikov algebras and show that it is characterized by a pre-Novikov bialgebra. We also introduce the notion of pre-Novikov Yang-Baxter equation, whose symmetric solutions can produce pre-Novikov bialgebras. Moreover, the operator forms of pre-Novikov Yang-Baxter equation are also investigated.