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1. CMB 2001 (vol 44 pp. 140)

Gotay, Mark J.; Grabowski, Janusz
On Quantizing Nilpotent and Solvable Basic Algebras
We prove an algebraic ``no-go theorem'' to the effect that a nontrivial \pa\ cannot be realized as an associative algebra with the commu\-ta\-tor bracket. Using it, we show that there is an obstruction to quantizing the \pa\ of polynomials generated by a nilpotent \ba\ on a \sm. This result generalizes \gr 's famous theorem on the impossibility of quantizing the Poisson algebra of polynomials on $\r^{2n}$. Finally, we explicitly construct a polynomial quantization of a \sm\ with a solvable \ba, thereby showing that the obstruction in the nilpotent case does not extend to the solvable case.

Categories:81S99, 58F06

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