CONTRACTIONS OF LIE-ALGEBRAS AND SEPARATION OF VARIABLES - 2-DIMENSIONAL HYPERBOLOID

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.