A two-parameter quantization of sl(2/1) and its finite-dimensional representations

Abstract

The Lie superalgebra sl(2/1) is quantized in its non-standard simple rod system, resulting in a two-parameter quantum superalgebra Uq1,q2(sl(2/1)). When the two parameters coincide, Uq1,q2(sl(2/1)) reduces to a one-parameter dependent Z2-graded Hopf algebra, which is algebraically equivalent, but coalgebraically inequivalent, to the standard Uq(sl(2/1)). The finite-dimensional irreducible representations of this two-parameter quantum superalgebra are explicitly constructed when both or one of q1 and q2 are considered as indeterminates, and cyclic representations are also obtained when both deformation parameters are roots of unity.