Kontsevich Deformation Quantization and Flat Connections |
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| Authors: | Anton Alekseev Charles Torossian |
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| Affiliation: | 1. Section de Mathématiques, Université de Genève, 2-4 Rue du Lièvre, C.P. 64, 1211, Genève 4, Switzerland
2. Institut Mathématiques de Jussieu, Université Paris 7, CNRS, Case 7012, 2 Place Jussieu, 75005, Paris, France
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| Abstract: | In Torossian (J Lie Theory 12(2):597–616, 2002), the second author used the Kontsevich deformation quantization technique to define a natural connection ω n on the compactified configuration spaces [`(C)]n,0{overline{C}_{n,0}} of n points on the upper half-plane. Connections ω n take values in the Lie algebra of derivations of the free Lie algebra with n generators. In this paper, we show that ω n is flat. |
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