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arXiv math-ph/99020121999-02math-phmath.MPmath.SGquant-ph

On Quantizing Nilpotent and Solvable Basic Algebras

Mark J. Gotay, Janusz Grabowski

备注：: 12 pages, Latex2e. Main result (Theorem 1) substantially strengthened; some rewriting
发表信息：: Canadian Math. Bull. 44 (2001), 140-149.

英文摘要：

We 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.

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