The Harish-Chandra homomorphism and representations of quantum superalgebra $U_{q}(\osp(1,2,\bc))$

Abstract

In this paper a new class of quantum algebra is constructed. It is a Hopf superalgebra and an extension of the quantized enveloping superalgebra of $\osp(1, 2)$. For these algebras, the  Harish-Chandra homomorphism when $q$ is not a root of unity is obtained.  All simple modules for an arbitrary  parameter $q$ are determined up to isomorphism .