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 GLp,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 GLq(2) (where p=q) induce corresponding calculi on the quantum subgroup SLq(2). It is shown that on SLq(2) there are only two different bicovariant differential calculi. From these one obtains the 4D+or- calculi on SUq(2). The classical limit of the two differential calculi on SLq(2) is investigated revealing a relation with recent work on deformed differential calculi on commutative (function) algebras.