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arXiv · 2404.13383

Quasi-Frobenius Novikov algebras and pre-Novikov bialgebras

Yue Li·Yanyong Hong
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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.

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Yue Li, Yanyong Hong. 2024-04-20. Quasi-Frobenius Novikov algebras and pre-Novikov bialgebras. https://arxiv.org/abs/2404.13383

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