Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles
Let λbe a finite-dimensional representation of a connected nilpotent group Gand Ube a unitary representation of G. We investigate the structure of the extensions of λby Uand, correspondingly, the group H1(λ, U)of 1-cohomologies. A spectral criterion of triviality of H1(λ, U)is proved and systematica...
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| Format: | Article |
| Language: | English |
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Elsevier
2015
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| Online Access: | https://repository.londonmet.ac.uk/1013/7/SECOND%20SUBMISSION%20TO%20JFA-15-137R1.pdf |
| _version_ | 1804071616254050304 |
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| author | Kissin, Edward Shulman, Victor S. |
| author_facet | Kissin, Edward Shulman, Victor S. |
| author_sort | Kissin, Edward |
| collection | LMU |
| description | Let λbe a finite-dimensional representation of a connected nilpotent group Gand Ube a unitary representation of G. We investigate the structure of the extensions of λby Uand, correspondingly, the group H1(λ, U)of 1-cohomologies. A spectral criterion of triviality of H1(λ, U)is proved and systematically used in the study of various types of decomposition of the extensions. We consider a special type of (λ, U)-cocycles – neutral cocycles, which play a crucial role in the theory of J-unitary representations of groups on Pontryagin Πk-spaces. |
| first_indexed | 2024-07-09T03:46:05Z |
| format | Article |
| id | oai:repository.londonmet.ac.uk:1013 |
| institution | London Metropolitan University |
| language | English |
| last_indexed | 2024-07-09T03:46:05Z |
| publishDate | 2015 |
| publisher | Elsevier |
| record_format | eprints |
| spelling | oai:repository.londonmet.ac.uk:10132020-05-29T16:27:50Z http://repository.londonmet.ac.uk/1013/ Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles Kissin, Edward Shulman, Victor S. 510 Mathematics Let λbe a finite-dimensional representation of a connected nilpotent group Gand Ube a unitary representation of G. We investigate the structure of the extensions of λby Uand, correspondingly, the group H1(λ, U)of 1-cohomologies. A spectral criterion of triviality of H1(λ, U)is proved and systematically used in the study of various types of decomposition of the extensions. We consider a special type of (λ, U)-cocycles – neutral cocycles, which play a crucial role in the theory of J-unitary representations of groups on Pontryagin Πk-spaces. Elsevier 2015-07-22 Article PeerReviewed text en https://repository.londonmet.ac.uk/1013/7/SECOND%20SUBMISSION%20TO%20JFA-15-137R1.pdf Kissin, Edward and Shulman, Victor S. (2015) Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles. Journal of Functional Analysis, 269 (8). pp. 2564-2610. ISSN 0022-1236 http://dx.doi.org/10.1016/j.jfa.2015.07.003 10.1016/j.jfa.2015.07.003 |
| spellingShingle | 510 Mathematics Kissin, Edward Shulman, Victor S. Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles |
| title | Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles |
| title_full | Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles |
| title_fullStr | Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles |
| title_full_unstemmed | Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles |
| title_short | Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles |
| title_sort | non unitary representations of nilpotent groups i cohomologies extensions and neutral cocycles |
| topic | 510 Mathematics |
| url | https://repository.londonmet.ac.uk/1013/7/SECOND%20SUBMISSION%20TO%20JFA-15-137R1.pdf |
| work_keys_str_mv | AT kissinedward nonunitaryrepresentationsofnilpotentgroupsicohomologiesextensionsandneutralcocycles AT shulmanvictors nonunitaryrepresentationsofnilpotentgroupsicohomologiesextensionsandneutralcocycles |