Combinatorial quantization of the Hamiltonian Chern-Simons theory I

@article{Alekseev1994CombinatorialQO,
  title={Combinatorial quantization of the Hamiltonian Chern-Simons theory I},
  author={A Alekseev and Harald Grosse and Volker Schomerus},
  journal={Communications in Mathematical Physics},
  year={1994},
  volume={172},
  pages={317-358}
}
Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *- operation and a positive inner product. 
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Recently we suggested a new quantum algebra, the moduli algebra, which was conjectured to be a quantum algebra of observables of the Hamiltonian Chern Simons theory. This algebra provides theExpand
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