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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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-147854 |
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dspace |
| spelling |
irk-123456789-1478542019-02-17T01:28:00Z A Duflo Star Product for Poisson Groups Brochier, A. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147854 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Brochier, A. |
| spellingShingle |
Brochier, A. A Duflo Star Product for Poisson Groups Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Brochier, A. |
| author_sort |
Brochier, A. |
| title |
A Duflo Star Product for Poisson Groups |
| title_short |
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_sort |
duflo star product for poisson groups |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147854 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT brochiera aduflostarproductforpoissongroups AT brochiera duflostarproductforpoissongroups |
| first_indexed |
2023-05-20T17:28:41Z |
| last_indexed |
2023-05-20T17:28:41Z |
| _version_ |
1796153386665508864 |