Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants
In this paper we prove a conjecture of B. Shoikhet. This conjecture states that the tangent isomorphism on homology, between the Poisson homology associated to a Poisson structure on Rd and the Hochschild homology of its quantized star-product algebra, is an isomorphism of modules over the (isomorph...
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| Date: | 2008 |
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| Main Authors: | , |
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| Language: | English |
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Інститут математики НАН України
2008
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Cite this: | Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants / D. Calaque and C.A. Rossi // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 13 назв. — англ. |
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oai:nasplib.isofts.kiev.ua:123456789-1490222025-02-23T17:32:25Z Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants Calaque, D. Rossi, C.A. In this paper we prove a conjecture of B. Shoikhet. This conjecture states that the tangent isomorphism on homology, between the Poisson homology associated to a Poisson structure on Rd and the Hochschild homology of its quantized star-product algebra, is an isomorphism of modules over the (isomorphic) respective cohomology algebras. As a consequence, we obtain a version of the Duflo isomorphism on coinvariants. This paper is a contribution to the Special Issue on Deformation Quantization. We thank Giovanni Felder for useful discussions and comments. The research of D.C. (on leave of absence from Universit´e Lyon 1) is fully supported by the European Union thanks to a Marie Curie Intra-European Fellowship (contract number MEIF-CT-2007-042212). 2008 Article Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants / D. Calaque and C.A. Rossi // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 13 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 16E45; 16E40; 81Q30 https://nasplib.isofts.kiev.ua/handle/123456789/149022 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
In this paper we prove a conjecture of B. Shoikhet. This conjecture states that the tangent isomorphism on homology, between the Poisson homology associated to a Poisson structure on Rd and the Hochschild homology of its quantized star-product algebra, is an isomorphism of modules over the (isomorphic) respective cohomology algebras. As a consequence, we obtain a version of the Duflo isomorphism on coinvariants. |
| format |
Article |
| author |
Calaque, D. Rossi, C.A. |
| spellingShingle |
Calaque, D. Rossi, C.A. Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Calaque, D. Rossi, C.A. |
| author_sort |
Calaque, D. |
| title |
Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants |
| title_short |
Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants |
| title_full |
Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants |
| title_fullStr |
Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants |
| title_full_unstemmed |
Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants |
| title_sort |
shoikhet's conjecture and duflo isomorphism on (co)invariants |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| citation_txt |
Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants / D. Calaque and C.A. Rossi // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 13 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT calaqued shoikhetsconjectureanddufloisomorphismoncoinvariants AT rossica shoikhetsconjectureanddufloisomorphismoncoinvariants |
| first_indexed |
2025-07-22T04:20:45Z |
| last_indexed |
2025-07-22T04:20:45Z |
| _version_ |
1838319451553923072 |