EXTENDED QUANTUM ENVELOPING ALGEBRAS OF sl(2)

摘要

In present paper we define a new kind of quantized enveloping algebranof sl(2). We denote this algebra by Ur,t, where r, t are two non-negative integers. It isna non-commutative and non-cocommutative Hopf algebra. If r = 0, then the algebranUr,t is isomorphic to a tensor product of the algebra of infinite cyclic group and thenusual quantum enveloping algebra of sl(2) as Hopf algebras. The representation of thisnalgebra is studied.