Polynomial deformations of enveloping algebra U(sl(2,ℂ))

Abstract

We define the polynomial deformation, Ûpt, of enveloping algebra U(sl(2,ℂ)) as an analogue of quantum group and construct a 'nice' set Devenp of parameters on which we described irreducible representations and classify the irreducible ones in terms of the highest weights. Also, we construct the Casimir elements and using them we see that every finite dimensional Ûpt-module is semisimple.