Bibliographic description (Zentralblatt)

882.58005 Schmuedgen, Konrad; Schueler, Axel
Left-covariant differential calculi on $SL\sb q(N)$. (English)
Budzynski, Robert (ed.) et al., Quantum groups and quantum spaces.
Lectures delivered during the minisemester, Warsaw, Poland, December 1,
1995. Warszawa: Polish Academy of Sciences,
Inst. of Mathematics, Banach Cent. Publ. 40, 185-191 (1997). MSC 2000: *46L85 46L87 81R50,
Reviewer: G.Landi


We study N^2-1 dimensional left-covariant differential calculi on
the quantum group SL_q(N). In this way we obtain four classes
of differential calculi which are algebraically much simpler as the bicovariant calculi.

The algebra generated by the left-invariant vector fields has only
quadratic-linear relations and posesses a Poincare-Birkhoff-Witt basis.
We use the concept of universal (higher order) differential calculus associated
with a given left-covariant first order differential calculus. It turns out that the
space of left-invariant k-forms has the same dimension as in the case of the
corresponding classical Lie group SL(N).