Symmetries of the Space of Linear Symplectic Connections
There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt moment map, the Ricci tensor, and a translational term. The cr...
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| Дата: | 2017 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148602 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Symmetries of the Space of Linear Symplectic Connections / D.J.F. Fox // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148602 |
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dspace |
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irk-123456789-1486022019-02-19T01:24:24Z Symmetries of the Space of Linear Symplectic Connections Fox, D.J.F. There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt moment map, the Ricci tensor, and a translational term. The critical points of a functional constructed from it interpolate between the equations for preferred symplectic connections and the equations for critical symplectic connections. The commutative algebra of formal sums of symmetric tensors on a symplectic manifold carries a pair of compatible Poisson structures, one induced from the canonical Poisson bracket on the space of functions on the cotangent bundle polynomial in the fibers, and the other induced from the algebraic fiberwise Schouten bracket on the symmetric algebra of each fiber of the cotangent bundle. These structures are shown to be compatible, and the required Lie algebras are constructed as central extensions of their linear combinations restricted to formal sums of symmetric tensors whose first order term is a multiple of the differential of its zeroth order term. 2017 Article Symmetries of the Space of Linear Symplectic Connections / D.J.F. Fox // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D20; 53D05; 53C05; 17B99 DOI:10.3842/SIGMA.2017.002 http://dspace.nbuv.gov.ua/handle/123456789/148602 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 |
There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt moment map, the Ricci tensor, and a translational term. The critical points of a functional constructed from it interpolate between the equations for preferred symplectic connections and the equations for critical symplectic connections. The commutative algebra of formal sums of symmetric tensors on a symplectic manifold carries a pair of compatible Poisson structures, one induced from the canonical Poisson bracket on the space of functions on the cotangent bundle polynomial in the fibers, and the other induced from the algebraic fiberwise Schouten bracket on the symmetric algebra of each fiber of the cotangent bundle. These structures are shown to be compatible, and the required Lie algebras are constructed as central extensions of their linear combinations restricted to formal sums of symmetric tensors whose first order term is a multiple of the differential of its zeroth order term. |
| format |
Article |
| author |
Fox, D.J.F. |
| spellingShingle |
Fox, D.J.F. Symmetries of the Space of Linear Symplectic Connections Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Fox, D.J.F. |
| author_sort |
Fox, D.J.F. |
| title |
Symmetries of the Space of Linear Symplectic Connections |
| title_short |
Symmetries of the Space of Linear Symplectic Connections |
| title_full |
Symmetries of the Space of Linear Symplectic Connections |
| title_fullStr |
Symmetries of the Space of Linear Symplectic Connections |
| title_full_unstemmed |
Symmetries of the Space of Linear Symplectic Connections |
| title_sort |
symmetries of the space of linear symplectic connections |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148602 |
| citation_txt |
Symmetries of the Space of Linear Symplectic Connections / D.J.F. Fox // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 20 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT foxdjf symmetriesofthespaceoflinearsymplecticconnections |
| first_indexed |
2023-05-20T17:29:45Z |
| last_indexed |
2023-05-20T17:29:45Z |
| _version_ |
1796153421081870336 |