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...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2008
Main Author: Butin, F.
Format: Article
Language:English
Published: Інститут математики НАН України 2008
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149019
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Hochschild Homology and Cohomology of Klein Surfaces / F. Butin // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 18 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1862713286051495936
author Butin, F.
author_facet Butin, F.
citation_txt Hochschild Homology and Cohomology of Klein Surfaces / F. Butin // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 18 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
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 2025-12-07T17:43:30Z
format Article
fulltext
id nasplib_isofts_kiev_ua-123456789-149019
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T17:43:30Z
publishDate 2008
publisher Інститут математики НАН України
record_format dspace
spelling Butin, F.
2019-02-19T13:06:06Z
2019-02-19T13:06:06Z
2008
Hochschild Homology and Cohomology of Klein Surfaces / F. Butin // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 18 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 53D55; 13D03; 30F50; 13P10
https://nasplib.isofts.kiev.ua/handle/123456789/149019
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.
This paper is a contribution to the Special Issue on Deformation Quantization. I would like to thank my thesis advisors Gadi Perets and Claude Roger for their ef ficient and likeable help, for their great availability, and for the time that they devoted to me all along this study. I also thank Daniel Sternheimer who paid attention to my work and the referees for their relevant remarks and their judicious advice. And I am grateful to Serge Parmentier for the rereading of my English text.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Hochschild Homology and Cohomology of Klein Surfaces
Article
published earlier
spellingShingle Hochschild Homology and Cohomology of Klein Surfaces
Butin, F.
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
url https://nasplib.isofts.kiev.ua/handle/123456789/149019
work_keys_str_mv AT butinf hochschildhomologyandcohomologyofkleinsurfaces