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On the Heisenberg invariance and the Elliptic Poisson tensors

G. Ortenzi
  • Function : Author
S. R. Tagne Pelap
  • Function : Author

Abstract

We study different algebraic and geometric properties of Heisenberg invariant Poisson polynomial quadratic algebras. We show that these algebras are unimodular. The elliptic Sklyanin-Odesskii-Feigin Poisson algebras $q_{n,k}(\mathcal E)$ are the main important example. We classify all quadratic $H-$invariant Poisson tensors on ${\mathbb C}^n$ with $n\leq 6$ and show that for $n\leq 5$ they coincide with the elliptic Sklyanin-Odesskii-Feigin Poisson algebras or with their certain degenerations.

Dates and versions

hal-00619673 , version 1 (06-09-2011)

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G. Ortenzi, V. Rubtsov, S. R. Tagne Pelap. On the Heisenberg invariance and the Elliptic Poisson tensors. 2010. ⟨hal-00619673⟩
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