That amounts to a limiting operation on a parameter of the Lie algebra, altering the structure constants of this Lie algebra in a nontrivial singular manner, under suitable circumstances.
[2][3] For example, the Lie algebra of the 3D rotation group SO(3), [X1, X2] = X3, etc., may be rewritten by a change of variables Y1 = εX1, Y2 = εX2, Y3 = X3, as The contraction limit ε → 0 trivializes the first commutator and thus yields the non-isomorphic algebra of the plane Euclidean group, E2 ~ ISO(2).
(This is isomorphic to the cylindrical group, describing motions of a point on the surface of a cylinder.
It is the little group, or stabilizer subgroup, of null four-vectors in Minkowski space.)
Similar limits, of considerable application in physics (cf.