On Deformations and Contractions of Lie Algebras
In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrat...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2006 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146177 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Deformations and Contractions of Lie Algebras / A. Fialowski, Marc de Montigny // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862747191508992000 |
|---|---|
| author | Fialowski, A. Marc de Montigny |
| author_facet | Fialowski, A. Marc de Montigny |
| citation_txt | On Deformations and Contractions of Lie Algebras / A. Fialowski, Marc de Montigny // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation, the converse is not true in general. Also we note that some Lie algebras belonging to parameterized families are singled out by the irreversibility of deformations and contractions. After reminding that global deformations of the Witt, Virasoro, and affine Kac-Moody algebras allow one to retrieve Lie algebras of Krichever-Novikov type, we contract the latter to find new infinite dimensional Lie algebras.
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| first_indexed | 2025-12-07T20:49:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146177 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:49:55Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fialowski, A. Marc de Montigny 2019-02-07T20:21:06Z 2019-02-07T20:21:06Z 2006 On Deformations and Contractions of Lie Algebras / A. Fialowski, Marc de Montigny // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 14 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 17B66; 17B67; 17B65; 17B56; 17B68; 14D15; 81T40 https://nasplib.isofts.kiev.ua/handle/123456789/146177 In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation, the converse is not true in general. Also we note that some Lie algebras belonging to parameterized families are singled out by the irreversibility of deformations and contractions. After reminding that global deformations of the Witt, Virasoro, and affine Kac-Moody algebras allow one to retrieve Lie algebras of Krichever-Novikov type, we contract the latter to find new infinite dimensional Lie algebras. Partial support was provided by a grant from NATO Hungary. AF is grateful to OTKA (Hungary) for grants T043641 and T043034. MdM acknowledges partial financial support from the Natural Sciences and Engineering Research Council of Canada, and the organizers of the Conference Symmetry in Nonlinear Mathematical Physics, held in Kyiv in June 2005. We thank both referees for their remarks and useful suggestions en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Deformations and Contractions of Lie Algebras Article published earlier |
| spellingShingle | On Deformations and Contractions of Lie Algebras Fialowski, A. Marc de Montigny |
| title | On Deformations and Contractions of Lie Algebras |
| title_full | On Deformations and Contractions of Lie Algebras |
| title_fullStr | On Deformations and Contractions of Lie Algebras |
| title_full_unstemmed | On Deformations and Contractions of Lie Algebras |
| title_short | On Deformations and Contractions of Lie Algebras |
| title_sort | on deformations and contractions of lie algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146177 |
| work_keys_str_mv | AT fialowskia ondeformationsandcontractionsofliealgebras AT marcdemontigny ondeformationsandcontractionsofliealgebras |