Quasi-Frobenius Novikov algebras and pre-Novikov bialgebras

2024/07/22 by Yue Li, Yanyong Hong · 4 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications

paper · doi:10.1080/00927872.2024.2376861

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.

Citations

• Left-symmetric conformal algebras and vertex algebras

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• Anti-pre-Poisson bialgebras and relative Rota-Baxter operators
• Quasi-triangular, factorizable anti-dendriform bialgebras and relative Rota-Baxter operators
• Infinite-dimensional pre-Lie bialgebras via affinization of pre-Novikov bialgebras

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• Infinite-dimensional pre-Lie bialgebras via affinization of pre-Novikov bialgebras
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