Quantization of Hamiltonian coactions via twist

Bieliavsky, Pierre;Esposito, Chiara;Nest, Ryszard
(2020) Journal of Symplectic Geometry — Vol. 18, n° 2, p. 385-408 (2020)

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  • Bieliavsky, Pierreorcid-logoUCLouvain
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  • Esposito, ChiaraUniversität Würzburg
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  • Nest, RyszardUniversitetsparken 5
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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.
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Bieliavsky, P., Esposito, C., & Nest, R. (2020). Quantization of Hamiltonian coactions via twist. Journal of Symplectic Geometry, 18(2), 385-408. https://doi.org/10.4310/jsg.2020.v18.n2.a2 (Original work published 2020)