Star product and star exponential (Q608042)

This paper introduces a family of star products, parameterized by the space of complex symmetric matrices. Let us recall that Omori-Maeda-Miyazaki-Yoshioka obtained a generalization of the well-known Moyal-Weyl product by means of complex symmetric matrices. In this work, the authors consider this generalization and review the relevant facts about topological spaces and star exponentials. Then, they study several examples where they obtained interesting results. The star exponential of these examples are also discussed.