In this talk, I will introduce a bialgebra theory for the Novikov algebra, namely the Novikov bialgebra, which is characterized by the fact that its affinization (by a quadratic right Novikov algebra) gives an infinite-dimensional Lie bialgebra. A Novikov bialgebra is also characterized as a Manin triple of Novikov algebras. The notion of Novikov Yang-Baxter equation is introduced, whose skew-symmetric solutions can be used to produce Novikov bialgebras and hence Lie bialgebras. These solutions also give rise to skewsymmetric solutions of the classical Yang-Baxter equation in the infinite-dimensional Lie algebras from the Novikov algebras. Moreover, a similar connection between Novikov bialgebras and Lie conformal bialgebras will be introduced.
This talk is based on joint works with Chengming Bai and Li Guo.
This video is part of the European Non-Associative Algebra Seminar series.
