On Quantizing Nilpotent and Solvable Basic Algebras

Canadian mathematical bulletin

关键词: symplectic manifold;    Lagrangian foliation;    affine connection;   

DOI  :  10.4153/CMB-2001-018-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We prove an algebraic ``no-go theorem'' to the effect that anontrivial pa cannot be realized as an associative algebra with thecommu-ta-tor bracket. Using it, we show that there is anobstruction to quantizing the pa of polynomials generated by anilpotent a on a sm. This result generalizes gr 's famoustheorem on the impossibility of quantizing the Poisson algebra ofpolynomials on $^{2n}$. Finally, we explicitly construct apolynomial quantization of a sm with a solvable a, thereby showingthat the obstruction in the nilpotent case does not extend to thesolvable case.

【 授权许可】

Unknown