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SIGMA, 2006, том 2, 048, 10 стр.
(Mi sigma76)
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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
On Deformations and Contractions of Lie Algebras
Alice Fialowskia, Marc de Montignyb a Institute of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117, Budapest, Hungary
b Campus Saint-Jean and Theoretical Physics Institute, University of Alberta, 8406 - 91 Street, Edmonton, Alberta, T6C 4G9, Canada
Аннотация:
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.
Ключевые слова:
Lie algebras; deformations; contractions; Kac–Moody algebras
DOI:
https://doi.org/10.3842/SIGMA.2006.048
Полный текст:
PDF файл (220 kB)
Полный текст:
http://emis.mi.ras.ru/.../Paper048
Список литературы:
PDF файл
HTML файл
Реферативные базы данных:
ArXiv:
math.RT/0605091
Тип публикации:
Статья
MSC: 17B66; 17B67; 17B65; 17B56; 17B68; 14D15; 81T40 Поступила: 24 февраля 2006 г.; в окончательном варианте 25 апреля 2006 г.; опубликована 3 мая 2006 г.
Язык публикации: английский
Образец цитирования:
Alice Fialowski, Marc de Montigny, “On Deformations and Contractions of Lie Algebras”, SIGMA, 2 (2006), 048, 10 pp.
Цитирование в формате AMSBIB
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Образцы ссылок на эту страницу:
http://mi.mathnet.ru/sigma76 http://mi.mathnet.ru/rus/sigma/v2/p48
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
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Nesterenko, M, “Contractions of low-dimensional Lie algebras”, Journal of Mathematical Physics, 47:12 (2006), 123515
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Fialowski, A, “Formal deformations, contractions and moduli spaces of Lie algebras”, International Journal of Theoretical Physics, 47:2 (2008), 561
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Draper C., Martin C., Viruel A., “Fine gradings on the Lie algebra d4”, Forum Math, 22:5 (2010), 863–877
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Calderon Martin A.J., Sanchez-Delgado J.M., “Weight Modules Over Split Lie Algebras”, Mod. Phys. Lett. A, 28:5 (2013), 1350008
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Moutsopoulos G., “Homogeneous Anisotropic Solutions of Topologically Massive Gravity with a Cosmological Constant and their Homogeneous Deformations”, Class. Quantum Gravity, 30:12 (2013), 125014
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Эта страница: | 232 | Полный текст: | 44 | Литература: | 40 |
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