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Globalizing L-infinity-automorphisms of the Schouten algebra of polyvector fields
Stockholm University, Faculty of Science, Department of Mathematics.
2013 (English)In: Differential geometry and its applications (Print), ISSN 0926-2245, E-ISSN 1872-6984, Vol. 31, no 2, 239-247 p.Article in journal (Refereed) Published
Abstract [en]

Recently, Willwacher showed that the Grothendieck-Teichmuller group GRT acts by L-infinity-automorphisms on the Schouten algebra of polyvector fields T-poly(R-d) on affine space R-d. In this article, we prove that a large class of L-infinity-automorphisms on T-poly(R-d), including Willwacher's, can be globalized. That is, given an L-infinity-automorphism of T-poly(R-d) and a general smooth manifold M with the choice of a torsion-free connection, we give an explicit construction of an L-infinity-automorphism of the Schouten algebra T-poly(M) on the manifold M, depending on the chosen connection. The method we use is the Fedosov trick.

Place, publisher, year, edition, pages
2013. Vol. 31, no 2, 239-247 p.
Keyword [en]
Deformation quantization, Polyvector fields, Fedosov quantization, Grothendieck-Teichmuller group
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-89996DOI: 10.1016/j.difgeo.2012.12.002ISI: 000317448000007OAI: oai:DiVA.org:su-89996DiVA: diva2:622150
Note

AuthorCount:1;

Available from: 2013-05-20 Created: 2013-05-20 Last updated: 2017-12-06Bibliographically approved

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