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Abstract The classical Yang-Baxter equation (CYBE) is the semi-classical limit of
the quantum Yang-Baxter equation, named after the physicists C.N. Yang and
R. Baxter. Its solution has inspired the remarkable works of Belavin, Drinfeld,
and others and the important notions of Lie bialgebras and Manin triples.
Motivated by the importance of the CYBE in the theory and applications of
Lie algebras, various analogs of the CYBE for other algebraic structures have
been extensively studied in recent years. In this talk, we will first review the
tensor and operator forms of the CYBE and their connections with the
Rota-Baxter operators. Then we will give a generalization of the CYBE in both
tensor and operator form to the vertex operator algebras, which provides us
with a parameter-independent Yang-Baxter equation whose solutions lie in
an infinite-dimensional vector space. Finally, we will discuss its relations with
the CYBE. No prior knowledge of Yang-Baxter equations is required. This talk is
based on a joint work with Chengming Bai and Li Guo.