###
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

###
Abstract:

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).