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Symmetry, Integrability and Geometry: Methods and Applications, 2008, Volume 4, 064, 26 pp.
DOI: https://doi.org/10.3842/SIGMA.2008.064 (Mi sigma317) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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
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DOI: https://doi.org/10.3842/SIGMA.2008.064
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.
Keywords: Hochschild cohomology; Hochschild homology; Klein surfaces; Groebner bases; quantization; star-products.
Received: April 9, 2008; in final form September 4, 2008; Published online September 17, 2008
Bibliographic databases:
Document Type: Article
MSC: 53D55; 13D03; 30F50; 13P10
Language: English
Citation: Frédéric Butin, “Hochschild Homology and Cohomology of Klein Surfaces”, SIGMA, 4 (2008), 064, 26 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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