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arXiv · 1911.03320

Nonabelian elliptic Poisson structures on projective spaces

A. Odesskii·V. Sokolov
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Abstract

We review nonabelian Poisson structures on affine and projective spaces over $\mathbb{C}$. We also construct a class of examples of nonabelian Poisson structures on $\mathbb{C} P^{n-1}$ for $n>2$. These nonabelian Poisson structures depend on a modular parameter $\tau\in\mathbb{C}$ and an additional descrete parameter $k\in\mathbb{Z}$, where $1\leq k<n$ and $k,n$ are coprime. The abelianization of these Poisson structures can be lifted to the quadratic elliptic Poisson algebras $q_{n,k}(\tau)$.

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BibTeXRIS

A. Odesskii, V. Sokolov. 2019-11-08. Nonabelian elliptic Poisson structures on projective spaces. https://arxiv.org/abs/1911.03320

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