Quantization of Hamiltonian coactions via twist

TL;DR

This paper develops a framework for quantizing Hamiltonian coactions of Hopf algebras with Drinfel'd twists, extending classical momentum maps to the quantum setting using Hopf algebra techniques.

Contribution

It introduces a method to quantize classical Hamiltonian actions with 2-cocycles by employing Drinfel'd twists, bridging classical and quantum symmetries.

Findings

Defined classical Hamiltonian actions compatible with 2-cocycles

Constructed quantum momentum maps from classical ones

Quantized momentum maps using Drinfel'd twist approach

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 stucture 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.