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On Deformations and Contractions of Lie Algebras
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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On Deformations and Contractions of Lie Algebras
Інший ID:
2000 Mathematics Subject Classification: 17B66; 17B67; 17B65; 17B56; 17B68; 14D15; 81T40
Посилання:
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.
Підтримка:
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
Дата:
2006
Переглядів:
452
Завантажень:
248
Анотація:
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.
