The Γ-equivariant form of the Berezin quantization of the upper half plane

Abstract

Introduction Definitions and outline of the proofs Berezin quantization of the upper half plane Smooth algebras associated to the Berezin quantization The Berezin quantization for quotient space $\mathbb H/\Gamma$ The covariant symbol in invariant Berezin quantization A cyclic 2-cocycle associated to a deformation quantization Bounded cohomology and the cyclic 2-cocycle of the Berezin's deformation quantization Bibliography.