Aa. Izmestev et al., CONTRACTIONS OF LIE-ALGEBRAS AND SEPARATION OF VARIABLES - 2-DIMENSIONAL HYPERBOLOID, International journal of modern physics A, 12(1), 1997, pp. 53-61
The Inonu-Wigner contraction from the Lorentz group O(2,1) to the Eucl
idean group E(2) is used to relate the separation of variables in the
Laplace-Beltrami operators on the two corresponding homogeneous spaces
. We consider the contractions on four levels: the Lie algebra, the co
mmuting sets of second order operators in the enveloping algebra of o(
2,1), the coordinate systems and some eigenfunctions of the Laplace-Be
ltrami operators.