Deformation Quantization of Poisson Structures Associated to Lie Algebroids
In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E*, where E → M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even symplectic, our construction gets along without Kontsevich's forma...
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| Дата: | 2009 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149144 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Deformation Quantization of Poisson Structures Associated to Lie Algebroids / N. Neumaier, S. Waldmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 44 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149144 |
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dspace |
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irk-123456789-1491442019-02-20T01:26:41Z Deformation Quantization of Poisson Structures Associated to Lie Algebroids Neumaier, N. Waldmann, S. In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E*, where E → M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even symplectic, our construction gets along without Kontsevich's formality theorem but is based on a generalized Fedosov construction. As the whole construction merely uses geometric structures of E we also succeed in determining the dependence of the resulting star products on these data in finding appropriate equivalence transformations between them. Finally, the concreteness of the construction allows to obtain explicit formulas even for a wide class of derivations and self-equivalences of the products. Moreover, we can show that some of our products are in direct relation to the universal enveloping algebra associated to the Lie algebroid. Finally, we show that for a certain class of star products on E* the integration with respect to a density with vanishing modular vector field defines a trace functional. 2009 Article Deformation Quantization of Poisson Structures Associated to Lie Algebroids / N. Neumaier, S. Waldmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 44 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 53D55; 53D17 http://dspace.nbuv.gov.ua/handle/123456789/149144 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 |
In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E*, where E → M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even symplectic, our construction gets along without Kontsevich's formality theorem but is based on a generalized Fedosov construction. As the whole construction merely uses geometric structures of E we also succeed in determining the dependence of the resulting star products on these data in finding appropriate equivalence transformations between them. Finally, the concreteness of the construction allows to obtain explicit formulas even for a wide class of derivations and self-equivalences of the products. Moreover, we can show that some of our products are in direct relation to the universal enveloping algebra associated to the Lie algebroid. Finally, we show that for a certain class of star products on E* the integration with respect to a density with vanishing modular vector field defines a trace functional. |
| format |
Article |
| author |
Neumaier, N. Waldmann, S. |
| spellingShingle |
Neumaier, N. Waldmann, S. Deformation Quantization of Poisson Structures Associated to Lie Algebroids Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Neumaier, N. Waldmann, S. |
| author_sort |
Neumaier, N. |
| title |
Deformation Quantization of Poisson Structures Associated to Lie Algebroids |
| title_short |
Deformation Quantization of Poisson Structures Associated to Lie Algebroids |
| title_full |
Deformation Quantization of Poisson Structures Associated to Lie Algebroids |
| title_fullStr |
Deformation Quantization of Poisson Structures Associated to Lie Algebroids |
| title_full_unstemmed |
Deformation Quantization of Poisson Structures Associated to Lie Algebroids |
| title_sort |
deformation quantization of poisson structures associated to lie algebroids |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149144 |
| citation_txt |
Deformation Quantization of Poisson Structures Associated to Lie Algebroids / N. Neumaier, S. Waldmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 44 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT neumaiern deformationquantizationofpoissonstructuresassociatedtoliealgebroids AT waldmanns deformationquantizationofpoissonstructuresassociatedtoliealgebroids |
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2023-05-20T17:32:25Z |
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2023-05-20T17:32:25Z |
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