Abstract
We review noncommutative Poisson structures on affine and projective spaces over C. We also construct a class of examples of noncommutative Poisson structures on CPn−1 for n>2. These noncommutative 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).
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