Bicovariant differential calculi on GLp,q(2) and quantum subgroups

Abstract

In a previous paper all bicovariant differential calculi on the two-parameter quantum group GL_p,q(2) were determined. In this work the authors elaborate some of their properties and discuss relations with work by other authors. Furthermore, they show that there are two different ways in which bicovariant differential calculi on GL_q(2) (where p=q) induce corresponding calculi on the quantum subgroup SL_q(2). It is shown that on SL_q(2) there are only two different bicovariant differential calculi. From these one obtains the 4D_+or- calculi on SU_q(2). The classical limit of the two differential calculi on SL_q(2) is investigated revealing a relation with recent work on deformed differential calculi on commutative (function) algebras.