The notion of contraction of a Lie algebra (also called a degeneration by some authors) was originally introduced by physicists as a tool to relate classical and quantum mechanics. Inoenue and Wigner used contractions attending to a particularization, namely, that a subalgebra remains fixed through the contraction. This concept, quite restrictive for some purposes, was later generalized by Saletan and Levy-Nahas. The relation between contractions and deformation theory is an important, but not fully exploited, question. It is indeed proven that contractions are always related to deformations, while the converse is generally false. Information about contractions can be used to analyze the geometry of orbits by the action of a general linear group, specifically for the study of irreducible components of the varieties L~n and N~n.
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