The Equitable Presentation for the Extended Quantum Algebra Uq(f(K, J))

Abstract

Let Uq(f(K, J)) be an extended quantum enveloping algebra associated to sl2. In this paper, we display an equitable presentation for Uq(f(K, J)), in which all generators appear on a more equal footing. We also show that the equitable generators Y and Z are not invertible. Moreover, we give a presentation for the positive even subalgebra of Uq(f(K, J)) by generators and relations.