Nonabelian elliptic Poisson structures on projective spaces
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 $q_{n,k}(\tau)$.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.03320
- arXiv:
- arXiv:1911.03320
- Bibcode:
- 2019arXiv191103320O
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Algebraic Geometry
- E-Print:
- Latex, 22 pages, prove of the main theorem is added