On Quantizing Nilpotent and Solvable Basic Algebras

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dc.creatorGotay, Mark J.
dc.creatorGrabowski, Janusz
dc.date1999-02-08
dc.date1999-03-14
dc.date.accessioned2026-07-07T04:32:41Z
dc.date.available2026-07-07T04:32:41Z
dc.descriptionWe prove an algebraic ``no-go theorem'' to the effect that a nontrivial Poisson algebra cannot be realized as an associative algebra with the commutator bracket. Using this, we show that there is an obstruction to quantizing the Poisson algebra of polynomials generated by a nilpotent basic algebra on a symplectic manifold. Finally, we explicitly construct a polynomial quantization of a symplectic manifold with a solvable basic algebra, thereby showing that the obstruction in the nilpotent case does not extend to the solvable case.
dc.description12 pages, Latex2e. Main result (Theorem 1) substantially strengthened; some rewriting
dc.identifierhttps://arxiv.org/abs/math-ph/9902012
dc.identifierhttp://arxiv.org/abs/math-ph/9902012
dc.identifierCanadian Math. Bull. 44 (2001), 140-149.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58280
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subjectQuantum Physics
dc.titleOn Quantizing Nilpotent and Solvable Basic Algebras
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