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SIGMA 4 (2008), 064, 26 pages arXiv:0804.4324
https://doi.org/10.3842/SIGMA.2008.064
Contribution to the Special Issue on Deformation Quantization
Hochschild Homology and Cohomology of Klein Surfaces
Frédéric Butin
Université de Lyon, Université Lyon 1, CNRS,
UMR5208, Institut Camille Jordan, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France
Received April 09, 2008, in final form September 04, 2008; Published online September 17, 2008
Abstract
Within the framework of deformation quantization, a
first step towards the study of star-products is the calculation
of Hochschild cohomology. The aim of this article is precisely to
determine the Hochschild homology and cohomology in two cases of
algebraic varieties. On the one hand, we consider singular curves
of the plane; here we recover, in a different way, a result proved
by Fronsdal and make it more precise. On the other hand, we are
interested in Klein surfaces. The use of a complex suggested
by Kontsevich and the help of Groebner bases allow us to solve the problem.
Key words:
Hochschild cohomology; Hochschild homology; Klein surfaces; Groebner bases; quantization; star-products.
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