BICOVARIANT DIFFERENTIAL CALCULI ON GLP,Q(2) AND QUANTUM SUBGROUPS

In a recent paper all bicovariant differential calculi on the two-parameter quantum group GL(p,q) (2) were determined. In this work we elaborate some of their properties and discuss relations with work by other authors. Furthermore, we 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+/- 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.