QUANTUM (2- A GLOBAL APPROACH(1) KINEMATICAL ALGEBRAS )

In this paper we give an approach to quantum deformations of the (2+1) kinematical Lie algebras within a scheme that simultaneously describe s all groups of motions of classical geometries in N = 3 dimensions. W e cover at once all the kinematical geometries including the quantum v ersions of Inonu-Wigner contractions, which are defined in a natural w ay and relate q-deformations as expected. We thus obtain some q-deform ations 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.