Oberseminar Deformationsquantisierung und Geometrie: Kaichuan Qi (Penn State University)

Abstract: The cotangent bundle of a Lie groupoid carries a canonical symplectic groupoid structure. We study how this structure can be deformed to accommodate magnetic symplectic forms. We introduce magnetic cotangent groupoids and characterize when the magnetic symplectic forms are multiplicative. We then explain how these structures arise naturally from central extensions of Lie groupoids via symplectic reduction. As an application, we discuss the Kac–Moody central extension of the loop group and its connection to an equivariant gerbe representing the Alekseev–Malkin–Meinrenken class.