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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.