Canonical forms for matrices of Saletan contractions

Abstract

We show that each Saletan (linear) contraction can be realized, up to change of bases of the initial and the target Lie algebras, by a matrix-function that is completely defined by a partition of the dimension of Fitting component of its value at the limit value of the contraction parameter. The codimension of the Fitting component and this partition constitute the signature of the Saletan contraction. We study Saletan contractions with Fitting component of maximal dimension and trivial one-part partition. All contractions of such kind in dimension three are completely classified.