Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields
Two examples of Diff⁺S¹-invariant closed two-forms obtained from forms on jet bundles, which does not admit equivariant moment maps are presented. The corresponding cohomological obstruction is computed and shown to coincide with a nontrivial Lie algebra cohomology class on H²(X(S¹)).
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149158 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields / R. Ferreiro Pérez, J. Muñoz Masqué // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Ferreiro Pérez, R. Muñoz Masqué, J. 2019-02-19T17:50:20Z 2019-02-19T17:50:20Z 2009 Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields / R. Ferreiro Pérez, J. Muñoz Masqué // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 58D15; 17B56; 22E65; 53D20; 53D30; 58A20 https://nasplib.isofts.kiev.ua/handle/123456789/149158 Two examples of Diff⁺S¹-invariant closed two-forms obtained from forms on jet bundles, which does not admit equivariant moment maps are presented. The corresponding cohomological obstruction is computed and shown to coincide with a nontrivial Lie algebra cohomology class on H²(X(S¹)). This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”. Part of this work started during the stay of the first author at Utah State University under the advice of Professor Ian Anderson. The computations were first obtained by using MAPLE package “Vessiot”. Supported by Ministerio de Ciencia e Innovaci´on of Spain under grant #MTM2008–01386. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields |
| spellingShingle |
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields Ferreiro Pérez, R. Muñoz Masqué, J. |
| title_short |
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields |
| title_full |
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields |
| title_fullStr |
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields |
| title_full_unstemmed |
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields |
| title_sort |
non-hamiltonian actions and lie-algebra cohomology of vector fields |
| author |
Ferreiro Pérez, R. Muñoz Masqué, J. |
| author_facet |
Ferreiro Pérez, R. Muñoz Masqué, J. |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Two examples of Diff⁺S¹-invariant closed two-forms obtained from forms on jet bundles, which does not admit equivariant moment maps are presented. The corresponding cohomological obstruction is computed and shown to coincide with a nontrivial Lie algebra cohomology class on H²(X(S¹)).
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149158 |
| citation_txt |
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields / R. Ferreiro Pérez, J. Muñoz Masqué // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ. |
| work_keys_str_mv |
AT ferreiroperezr nonhamiltonianactionsandliealgebracohomologyofvectorfields AT munozmasquej nonhamiltonianactionsandliealgebracohomologyofvectorfields |
| first_indexed |
2025-12-07T13:15:09Z |
| last_indexed |
2025-12-07T13:15:09Z |
| _version_ |
1850855453697769472 |