In this paper we provide a quantization via formality of Poisson actions of a triangular Lie algebra on a smooth manifold . Using the formality of -polydifferential operators for Lie algebroids over , we obtain a deformation quantization of together with a quantum group and a map of associated DGLA's. This motivates a definition of quantum action in terms of -morphisms which generalizes the well-known definition given by Drinfeld.
Cite this article
Chiara Esposito, Niek de Kleijn, Universal deformation formula, formality and actions. J. Noncommut. Geom. 16 (2022), no. 2, pp. 423–453DOI 10.4171/JNCG/478