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A combinatorial approach to coefficients in deformation quantization

Lucian M. Ionescu
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Abstract

Graph cocycles for star-products are investigated from the combinatorial point of view, using Connes-Kreimer renormalization techniques. The Hochschild complex, controlling the deformation theory of associative algebras, is the ``Kontsevich representation'' of a DGLA of graphs coming from a pre-Lie algebra structure defined by graph insertions. Properties of the dual of its UEA (an odd parity analog of Connes-Kreimer Hopf algebra), are investigated in order to find solutions of the deformation equation. The solution of the initial value deformation problem, at tree-level, is unique. For linear coefficients the resulting formulas are relevant to the Hausdorff series.

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Lucian M. Ionescu. 2004-04-21. A combinatorial approach to coefficients in deformation quantization. https://arxiv.org/abs/math/0404389

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