2024/07/22 by Yue Li, Yanyong Hong · 4 citations
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Mathematics #Novikov self-consistency principle #Pure mathematics
paper · doi:10.1080/00927872.2024.2376861
published in Communications in Algebra 53(1), 308-327 (Taylor & Francis)
openalex publication_date 2024/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25
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.