We discuss non-abelian Poisson structures on affine and projective spaces over ℂ. We also construct a class of examples of non-abelian Poisson structures on ℂPn-1 for n ≥ 3. These non-abelian Poisson structures depend on a modular parameter τ ∈ ℂ and an additional discrete parameter k ∈ ℤ, where 1 ≤ k < n and k,n are coprime. The abelianization of these Poisson structures can be lifted to the quadratic elliptic Poisson algebras qn,k(τ).
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
