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Star products and applications. (English) Zbl 1216.53081

Summary: Star products parametrized by complex matrices are defined. Especially commutative associative star products are treated, and star exponentials with respect to these star products are considered. Jacobi’s theta functions are given as infinite sums of star exponentials. As application, several concrete identities are obtained by properties of the star exponentials.

MSC:

53D55 Deformation quantization, star products
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