On Deformations and Contractions of Lie Algebras

Details On Deformations and Contractions of Lie Algebras On Deformations and Contractions of Lie Algebras

2006-05-03

arxiv.org/abs/math/0605091v1

SIGMA 2 (2006), 048, 10 pages

Mathematics

Representation Theory

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2006.048

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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