The quantized universal enveloping algebras Uq(iso(N)), Uq(e(3,1)) and Uq(e(N)) and the representation theory of Uq(e(3))

Abstract

We construct the Hopf algebras of Uq(iso(N)) and Uq(iso(3,1)) as regular functionals on their function algebras, examine the possible *-involutions on these objects, derive the quantized Euclidean algebras Uq(e(N)), and finally give the irreducible representations of Uq(e(3)) depending on two parameters which fix the value of the Casimir operators.