A Duflo Star Product for Poisson Groups
Let G be a finite-dimensional Poisson algebraic, Lie or formal group. We show that the center of the quantization of G provided by an Etingof-Kazhdan functor is isomorphic as an algebra to the Poisson center of the algebra of functions on G. This recovers and generalizes Duflo's theorem which g...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2016 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147854 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Duflo Star Product for Poisson Groups / A. Brochier // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 21 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734520051040256 |
|---|---|
| author | Brochier, A. |
| author_facet | Brochier, A. |
| citation_txt | A Duflo Star Product for Poisson Groups / A. Brochier // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let G be a finite-dimensional Poisson algebraic, Lie or formal group. We show that the center of the quantization of G provided by an Etingof-Kazhdan functor is isomorphic as an algebra to the Poisson center of the algebra of functions on G. This recovers and generalizes Duflo's theorem which gives an isomorphism between the center of the enveloping algebra of a finite-dimensional Lie algebra a and the subalgebra of ad-invariant in the symmetric algebra of a. As our proof relies on Etingof-Kazhdan construction it ultimately depends on the existence of Drinfeld associators, but otherwise it is a fairly simple application of graphical calculus. This shed some lights on Alekseev-Torossian proof of the Kashiwara-Vergne conjecture, and on the relation observed by Bar-Natan-Le-Thurston between the Duflo isomorphism and the Kontsevich integral of the unknot.
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| first_indexed | 2025-12-07T19:43:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147854 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:43:22Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Brochier, A. 2019-02-16T09:18:49Z 2019-02-16T09:18:49Z 2016 A Duflo Star Product for Poisson Groups / A. Brochier // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20G42; 17B37; 53D55 DOI:10.3842/SIGMA.2016.088 https://nasplib.isofts.kiev.ua/handle/123456789/147854 Let G be a finite-dimensional Poisson algebraic, Lie or formal group. We show that the center of the quantization of G provided by an Etingof-Kazhdan functor is isomorphic as an algebra to the Poisson center of the algebra of functions on G. This recovers and generalizes Duflo's theorem which gives an isomorphism between the center of the enveloping algebra of a finite-dimensional Lie algebra a and the subalgebra of ad-invariant in the symmetric algebra of a. As our proof relies on Etingof-Kazhdan construction it ultimately depends on the existence of Drinfeld associators, but otherwise it is a fairly simple application of graphical calculus. This shed some lights on Alekseev-Torossian proof of the Kashiwara-Vergne conjecture, and on the relation observed by Bar-Natan-Le-Thurston between the Duflo isomorphism and the Kontsevich integral of the unknot. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Duflo Star Product for Poisson Groups Article published earlier |
| spellingShingle | A Duflo Star Product for Poisson Groups Brochier, A. |
| title | A Duflo Star Product for Poisson Groups |
| title_full | A Duflo Star Product for Poisson Groups |
| title_fullStr | A Duflo Star Product for Poisson Groups |
| title_full_unstemmed | A Duflo Star Product for Poisson Groups |
| title_short | A Duflo Star Product for Poisson Groups |
| title_sort | duflo star product for poisson groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147854 |
| work_keys_str_mv | AT brochiera aduflostarproductforpoissongroups AT brochiera duflostarproductforpoissongroups |