Generalized AKS Scheme of Integrability Via Vertex Algebra (Wenda FANG, RIMS Kyoto)

04.06.2024 15:30 – 16:30

There is a well-known way to construct integrable systems via Lie algebra called the Adler-Kostant-Symes (AKS) scheme. Let g be a Lie algebra with an invariant, non-degenerate bilinear form ⟨ , ⟩. Let R be a classical Rmatrix of g, this gives a modified Lie algebra gR. Consider the Kirillov-Kostant Poisson structures on the g∗ and g∗R and denote Poisson brackets on g∗ and g∗R by { , } and { , }R, respectively. Then all functions in the Poisson center with respect to { , } are commute with respect to { , }R.
In this talk, we define the classical R-matrix for the vertex Lie algebras. We will see that a sufficient condition for an operator on a vertex Lie algebra to be a classical R-matrix is the modified Yang-Baxter equation (mYBE) of vertex Lie algebra which is an analog of the mYBE of Lie algebra. By using this R-matrix of vertex Lie algebra, we give a new scheme of integrability.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre