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SIGMA, 2006, Volume 2, 048, 10 pages (Mi sigma76)  

This article is cited in 5 scientific papers (total in 5 papers)

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

Abstract: 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.

Keywords: Lie algebras; deformations; contractions; Kac–Moody algebras

DOI: https://doi.org/10.3842/SIGMA.2006.048

Full text: PDF file (220 kB)
Full text: http://emis.mi.ras.ru/.../Paper048
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Bibliographic databases:

ArXiv: math.RT/0605091
MSC: 17B66; 17B67; 17B65; 17B56; 17B68; 14D15; 81T40
Received: February 24, 2006; in final form April 25, 2006; Published online May 3, 2006
Language:

Citation: Alice Fialowski, Marc de Montigny, “On Deformations and Contractions of Lie Algebras”, SIGMA, 2 (2006), 048, 10 pp.

Citation in format AMSBIB
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\by Alice Fialowski, Marc de Montigny
\paper On Deformations and Contractions of Lie Algebras
\jour SIGMA
\yr 2006
\vol 2
\papernumber 048
\totalpages 10
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Nesterenko, M, “Contractions of low-dimensional Lie algebras”, Journal of Mathematical Physics, 47:12 (2006), 123515  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Fialowski, A, “Formal deformations, contractions and moduli spaces of Lie algebras”, International Journal of Theoretical Physics, 47:2 (2008), 561  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Draper C., Martin C., Viruel A., “Fine gradings on the Lie algebra d4”, Forum Math, 22:5 (2010), 863–877  crossref  mathscinet  zmath  isi  elib  scopus
    4. Calderon Martin A.J., Sanchez-Delgado J.M., “Weight Modules Over Split Lie Algebras”, Mod. Phys. Lett. A, 28:5 (2013), 1350008  crossref  mathscinet  zmath  isi  scopus
    5. Moutsopoulos G., “Homogeneous Anisotropic Solutions of Topologically Massive Gravity with a Cosmological Constant and their Homogeneous Deformations”, Class. Quantum Gravity, 30:12 (2013), 125014  crossref  mathscinet  zmath  adsnasa  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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