Quantum (2+1) kinematical algebras: a global approach

Abstract

In this paper we give an approach to quantum deformations of the (2+1) kinematical Lie algebras within a scheme that simultaneously describes all groups of motions of classical geometries in N=3 dimensions. We cover at once all the kinematical geometries including the quantum versions of Inonu-Wigner contractions, which are defined in a natural way and relate q-deformations as expected. We thus obtain some q-deformations previously known for the three-dimensional Euclidean and (2+1)-Poincare algebras and also some new q-deformations for these and other kinematical algebras, such as the (2+1)-de Sitter, Galilei and Newton-Hooke algebras.