Deformation quantization for actions of Kählerian lie groups - Bieliavsky, Pierre, 1970-; Gayral, V. (Victor), 1979- (Memoirs of the American Mathematical Society, 2015)
Let \mathbb{B} be a Lie group admitting a left-invariant negatively curved Kählerian structure. Consider a strongly continuous action α of \mathbb{B} on a Fréchet algebra \mathcal{A}. Denote by \mathcal{A}^∞ the associated Fréchet algebra of smooth vectors for this action. In the Abelian case \mathbb{B}=\mathbb{R}^{2n} and α isometric, Marc Rieffel proved that Weyl's operator symbol composition formula (the so called Moyal product) yields a deformation through Fréchet algebra structures \{\star_{θ}^α\}_{θ\in\mathbb{R}} on \mathcal{A}^∞. When \mathcal{A} is a.