Journal of Symplectic Geometry

Volume 18 (2020)

Number 2

Quantization of Hamiltonian coactions via twist

Pages: 385 – 408

DOI: https://dx.doi.org/10.4310/JSG.2020.v18.n2.a2

Authors

Pierre Bieliavsky (Faculté des Sciences, Ecole de Mathématique, Institut de Recherche en Mathématique et Physique, Louvain-la-Neuve, Belgium)

Chiara Esposito (Dipartimento di Matematica, Università degli Studi di Salerno, Fisciano (Salerno), Italy)

Ryszard Nest (Institut for Matematiske Fag, Københavns Universitet, Københavns, Denmark)

Abstract

In this paper we introduce a notion of quantum Hamiltonian (co)action of Hopf algebras endowed with Drinfel’d twist structure (resp., 2-cocycles). First, we define a classical Hamiltonian action in the setting of Poisson Lie groups compatible with the 2-cocycle structure and we discuss a concrete example. This allows us to construct, out of the classical momentum map, a quantum momentum map in the setting of Hopf coactions and to quantize it by using Drinfel’d approach.

Received 11 June 2018

Accepted 30 April 2019

Published 8 June 2020