A combinatorial approach to coefficients in deformation quantization

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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.
23 pages, AMS LaTeX, 8 eps figures

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Quantum Algebra, Mathematical Physics, 53D55; 81T18

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http://salesiana.dossiersoluciones.com/handle/123456789/70928

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0404389
 http://arxiv.org/abs/math/0404389

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arXiv