On the $Γ$-equivariant form of the Berezin's quantization of the upper half plane

Physics – High Energy Physics – High Energy Physics - Theory

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Let $\Gamma$ be a fuchsian subgroup of \pslr. In this paper we consider the $\Gamma$-equivariant form of the Berezin's quantization of the upper half plane which will correspond to a deformation quantization of the (singular) space $\Bbb H/\Gamma$. Our main result is that the von Neumann algebra associated to the $\Gamma-$ equivariant form of the quantization is stable isomorphic with the von Neumann algebra associated to $\Gamma$.

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