Classification of Left-Covariant Differential Calculi on the Quantum Group $\SLq 2$
Abstract
Description
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 $Γ$ are determined and investigated for which the left-invariant differential one-forms $ω(u^1_2)$, $ω(u^2_1)$ and $ω(u^1_1-u^2_2)$ generate $Γ$ 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
LaTeX2e, 43 pages, to appear in Journal of Algebra
LaTeX2e, 43 pages, to appear in Journal of Algebra