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.

Ortenzi, G., Rubtsov, V., Pelap, S. (2011). On the Heisenberg Invariance and the Elliptic Poisson Tensors. LETTERS IN MATHEMATICAL PHYSICS, 96(1-3), 263-284 [10.1007/s11005-010-0433-1].

On the Heisenberg Invariance and the Elliptic Poisson Tensors

ORTENZI, GIOVANNI
;
2011

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.
Articolo in rivista - Articolo scientifico
Heisenberg group; Poisson algebras; Sklyanin elliptic algebras; unimodular class; Mathematical Physics; Statistical and Nonlinear Physics
English
2011
96
1-3
263
284
none
Ortenzi, G., Rubtsov, V., Pelap, S. (2011). On the Heisenberg Invariance and the Elliptic Poisson Tensors. LETTERS IN MATHEMATICAL PHYSICS, 96(1-3), 263-284 [10.1007/s11005-010-0433-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/56547
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