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    On the Heisenberg invariance and the Elliptic Poisson tensors

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    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 qn,k(E)q_{n,k}(\mathcal E) are the main important example. We classify all quadratic H−H-invariant Poisson tensors on Cn{\mathbb C}^n with n≤6n\leq 6 and show that for n≤5n\leq 5 they coincide with the elliptic Sklyanin-Odesskii-Feigin Poisson algebras or with their certain degenerations.Comment: 14 pages, no figures, minor revision, typos correcte
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