Quantization of Poisson Hopf algebras

2019/06/25 by Pulmann, Ján, Ševera, Pavol · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1906.10616

Abstract

We describe a method for quantization of Poisson Hopf algebras in \mathbb Q-linear symmetric monoidal categories. It is compatible with tensor products and can also be used to produce braided Hopf algebras. The main idea comes from the fact that nerves of groups are symmetric simplicial sets. Nerves of Hopf algebras then turn out to be braided rather than symmetric and nerves of Poisson Hopf algebras to be infinitesimally braided. The problem is thus solved via the standard machinery of Drinfeld associators.

Cited by

• Quantization of infinitesimal braidings and pre-Cartier quasi-bialgebras

Related

• Calculus and Quantizations over Hopf algebras
• Hopf actions on Poisson algebras
• Poisson algebras associated to quasi-Hopf algebras
• Quantization of pencils with a gl-type Poisson center and braided geometry
• Quantization of a Poisson structure on products of principal affine spaces