Classification of Left-Covariant Differential Calculi on the Quantum Group $\SLq 2$
Abstract
For transcendental values of q the quantum tangent spaces of all left-covariant first order differential calculi of dimension less than four on the quantum group $\SLq 2$ are given. All such differential calculi $\Gamma $ are determined and investigated for which the left-invariant differential one-forms $\omega (u^1_2)$, $\omega (u^2_1)$ and $\omega (u^1_1-u^2_2)$ generate $\Gamma $ as a bimodule and the universal higher order differential calculus has the same dimension as in the classical case. Important properties (cohomology spaces, *-structures, braidings, generalized Lie brackets) of these calculi are examined as well. Keywords: quantum groups, noncommutative differential calculus, quantum tangent space
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- June 2000
- DOI:
- 10.48550/arXiv.math/0006211
- arXiv:
- arXiv:math/0006211
- Bibcode:
- 2000math......6211H
- Keywords:
-
- Mathematics - Quantum Algebra;
- 17B37;
- 46L87;
- 81R50
- E-Print:
- LaTeX2e, 43 pages, to appear in Journal of Algebra