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Fréchet algebraic deformation quantization. (English) Zbl 1290.53079
This work constructs a star product on the Poincaré disk in order to produce a Fréchet topology making the star product continuous. First, two constructions are proposed. Several basic examples are discussed to illustrate the general construction. The example of the Poincaré disk is then studied in details. In this example, the properties of the corresponding Fréchet algebra are studied. The basic properties of the Poincaré disk and all the relevant classical results are also recalled in the paper.

53D55 Deformation quantization, star products
81T70 Quantization in field theory; cohomological methods
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