Universal deformation formula, formality and actions

Journal of noncommutative geometry

article

Chiara Esposito¹  Niek de Kleijn² 

[1] Università degli Studi di Salerno;Université Libre de Bruxelles CP 218

关键词: Poisson action;    formality;    L -morphism;    twisting;   

DOI  :  10.4171/jncg/478

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

In this paper we provide a quantization via formality of Poisson actions of a triangular Lie algebra (g,r)(\mathfrak{g},r)(g,r) on a smooth manifold MMM. Using the formality of EEE-polydifferential operators for Lie algebroids EEE over MMM, we obtain a deformation quantization of MMM together with a quantum group Uρℏ(g)\mathscr{U}_{\rho_\hbar}(\mathfrak{g})Uρℏ​​(g) and a map of associated DGLA's. This motivates a definition of quantum action in terms of L∞L_\inftyL∞​-morphisms which generalizes the well-known definition given by Drinfeld.

【 授权许可】

CC BY