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(ε) are the main important example. We classify all quadratic H-invariant Poisson tensors on ℂn with n ≤ 6 and show that for n ≤ 5 they coincide with the elliptic Sklyanin-Odesskii-Feigin Poisson algebras or with their certain degenerations. © 2010 Springer.
On the Heisenberg Invariance and the Elliptic Poisson Tensors
ORTENZI, GIOVANNI;
2011-01-01
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 qn,k(ε) are the main important example. We classify all quadratic H-invariant Poisson tensors on ℂn with n ≤ 6 and show that for n ≤ 5 they coincide with the elliptic Sklyanin-Odesskii-Feigin Poisson algebras or with their certain degenerations. © 2010 Springer.
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