Hochschild Homology and Cohomology of Klein Surfaces
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 si...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2008-09-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2008.064 |
| _version_ | 1818154126011269120 |
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| author | Frédéric Butin |
| author_facet | Frédéric Butin |
| author_sort | Frédéric Butin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T14:21:33Z |
| format | Article |
| id | doaj.art-adf7f8c22ce14552a3e6ff1108696414 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-11T14:21:33Z |
| publishDate | 2008-09-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-adf7f8c22ce14552a3e6ff11086964142022-12-22T01:02:54ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592008-09-014064Hochschild Homology and Cohomology of Klein SurfacesFrédéric ButinWithin 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.http://dx.doi.org/10.3842/SIGMA.2008.064Hochschild cohomologyHochschild homologyKlein surfacesGroebner basesquantizationstar-products |
| spellingShingle | Frédéric Butin Hochschild Homology and Cohomology of Klein Surfaces Symmetry, Integrability and Geometry: Methods and Applications Hochschild cohomology Hochschild homology Klein surfaces Groebner bases quantization star-products |
| title | Hochschild Homology and Cohomology of Klein Surfaces |
| title_full | Hochschild Homology and Cohomology of Klein Surfaces |
| title_fullStr | Hochschild Homology and Cohomology of Klein Surfaces |
| title_full_unstemmed | Hochschild Homology and Cohomology of Klein Surfaces |
| title_short | Hochschild Homology and Cohomology of Klein Surfaces |
| title_sort | hochschild homology and cohomology of klein surfaces |
| topic | Hochschild cohomology Hochschild homology Klein surfaces Groebner bases quantization star-products |
| url | http://dx.doi.org/10.3842/SIGMA.2008.064 |
| work_keys_str_mv | AT fredericbutin hochschildhomologyandcohomologyofkleinsurfaces |