On Deformations and Contractions of Lie Algebras

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dc.creatorFialowski, Alice
dc.creatorde Montigny, Marc
dc.date2006-05-03
dc.date.accessioned2026-07-07T09:34:31Z
dc.date.available2026-07-07T09:34:31Z
dc.descriptionIn 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.
dc.descriptionPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math/0605091
dc.identifierhttp://arxiv.org/abs/math/0605091
dc.identifierSIGMA 2 (2006), 048, 10 pages
dc.identifierdoi:10.3842/SIGMA.2006.048
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159520
dc.subjectRepresentation Theory
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.titleOn Deformations and Contractions of Lie Algebras
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