Abstract
Star products with a real deformation parameter ℏ are considered. By means of complex symmetric matrices {K}, a family of star products {∗K} is given on the space of complex polynomials. By taking completion of the set of polynomials, star products are extended to star products on the spaces of certain entire functions. Then one can construct star exponential functions in these spaces, which produce various interesting identities. As an example, Clifford algebras are constructed explicitly in terms of the extended star product algebra.
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