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Lie Group Quantum Mathematics Seminar

Yang-Baxter equations for vertex operator algebras and their operator forms

Jianqi Liu, University of California at Santa Cruz

Location:  Hill 705
Date & time: Friday, 07 April 2023 at 12:10PM - 1:10PM

Abstract The classical Yang-Baxter equation (CYBE) is the semi-classical limit ofthe quantum Yang-Baxter equation, named after the physicists C.N. Yang andR. 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 ofLie algebras, various analogs of the CYBE for other algebraic structures havebeen extensively studied in recent years. In this talk, we will first review thetensor and operator forms of the CYBE and their connections with theRota-Baxter operators. Then we will give a generalization of the CYBE in bothtensor and operator form to the vertex operator algebras, which provides uswith a parameter-independent Yang-Baxter equation whose solutions lie inan infinite-dimensional vector space. Finally, we will discuss its relations withthe CYBE. No prior knowledge of Yang-Baxter equations is required. This talk isbased on a joint work with Chengming Bai and Li Guo.

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