Jonas Schnitzer:
Quantization of momentum maps and adapted formality morphisms
Time and place
Monday, 27.5.24, 16:00-17:00, Raum 125, Ernst-Zermelo-Str. 1
Abstract
If a Lie group acts on a Poisson manifold by Hamiltonian symmetries there is a well-understood way to get rid of unnecessary degrees of freedom and pass to a Poisson manifold of a lower dimension. This procedure is known as Poisson-Hamiltonian reduction. There is a similar construction for invariant star products admitting a quantum momentum map, which leads to a deformation quantization of the Poisson-Hamiltonian reduction of the classical limit. \n\nThe existence of quantum momentum maps is only known in very few cases, like linear Poisson structures and symplectic manifolds. The aim of this talk is to fill this gap and show that there is a universal way to find quantized momentum maps using so-called adapted formality morphisms which exist, if one considers nice enough Lie group actions. This is a joint work with Chiara Esposito, Ryszard Nest and Boris Tsygan.