Construction of Some Hopf Algebras

Abstract

In this article the author considers those q deformed Hopfalgebras whose q=1 limits are the usual kinematical symmetrygroups, namely, the Euclidean, Poincare, Galilei and Lorentzones, which are noncompact or inhomogeneous or both. The methodof investigation is an extension to the q deformed Hopfstructure of the contraction procedure defined many years ago onthe Lie algebras, effective on their representations also. Theq deformed Hopf structures recovered at the end of this processare associated under the q=1 limit to nonsemisimple Liealgebras and in some cases it has been possible to obtain theuniversal R matrix associated to the nonsemisimple quantumalgebra.\par {For the entire collection see MR\Cite{Gielerak92:Quantum:Kluwer}[93h:00021].}