THE QUANTIZATION OF MOMENTUM MAPS AND ADAPTED FORMALITY MORPHISMS

Speaker(s)

JONAS SCHNITZER

Affiliation

Università di Pavia, Italy

Language of the talk

English

Date

Nov. 13, 2024, 5:15 p.m.

Link

https://uw-edu-pl.zoom.us/j/95105055663?pwd=TTIvVkxmMndhaHpqMFUrdm8xbzlHdz09

Title in Polish

THE QUANTIZATION OF MOMENTUM MAPS AND ADAPTED FORMALITY MORPHISMS

Seminar

North Atlantic Noncommutative Geometry Seminar

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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 the 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. The 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 for good enough Lie-group actions. This is a work in progress with Chiara Esposito, Ryszard Nest and Boris Tsygan.

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