A convergent star product for linear Poisson structures |
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Authors: | N Ben Amar M Hfaiedh |
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Institution: | (1) Department of Mathematics, Faculty of Sciences, BP 802, 3018 Sfax, Tunisia;(2) Department of Mathematics, Preparatory Institute of Technical and Scientific Studies, Sfax, Tunisia |
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Abstract: | An explicit star product ⋆
α
Γ
on the dual of a general Lie algebra equipped with the linear Poisson bracket is constructed. An equivalence operator between
this star product and the Kontsevich star product in K1] is given and diverse properties of the star product ⋆
α
Γ
are studied. It is also proved that the star product ⋆
α
Γ
provides a convergent deformation quantization in the sense of Rieffel R1]. |
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Keywords: | |
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