Contractions of Lie algebras and separation of variables. From two- dimensional hyperboloid to pseudo-Euclidean plane

摘要

The Inonu-Wigner contraction from the rotation group O(2,1) to the pseudo- Euclidean group E(1, 1) is used to relate the separation of variables in the Laplace-Beltrami operators on two corresponding homogeneous spaces. We consider the contractions on four levels: the Lie algebra, the commuting sets of the second order operators in the enveloping algebra of o(2,1), the coordinate systems and some eigenfunctions of the Laplace-Beltrami operators 8 refs., 2 tabs. Submitted to the Conference 'Quantum Groups. Deformations and Contractions', Bogazichi University, 17-24 Sep 1997, Istanbul, Turkey.