Classifying Morita equivalent star products. (English) Zbl 1323.53088

Bursztyn, Henrique; Waldmann, Stefan

Cortiñas, Guillermo (ed.), Topics in noncommutative geometry. Third Luis Santaló winter school – CIMPA research school on noncommutative geometry, Universidad de Buenos Aires, Buenos Aires, Argentina, July 26–August 6, 2010. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-6864-5/pbk). Clay Mathematics Proceedings 16, 1-17 (2012).

This paper is organized in the same way as the lectures given by the authors at CIMPA’s school ‘Topics in non commutative geometry’. The authors first recall the main results concerning deformation quantizations theory and star products. The notion of Morita equivalence is then explained in detail. Then the authors describe the Morita equivalence for star product as orbits of a suitable group action. The B-field action on formal structures and the Morita equivalence via Kontsevich’s classes are then studied.
For the entire collection see [Zbl 1254.00025].

Reviewer: Angela Gammella-Mathieu (Metz)

MSC:

53D17	Poisson manifolds; Poisson groupoids and algebroids
53D55	Deformation quantization, star products

Keywords:

Morita equivalences; classification; deformation quantization algebras; non commutative geometry; Kontsevich’s classes