Classification of Left-Covariant Differential Calculi on the Quantum Group $\SLq 2$

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dc.creatorHeckenberger, I.
dc.date2000-06-28
dc.date.accessioned2026-07-07T04:36:08Z
dc.date.available2026-07-07T04:36:08Z
dc.descriptionFor 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
dc.descriptionLaTeX2e, 43 pages, to appear in Journal of Algebra
dc.identifierhttps://arxiv.org/abs/math/0006211
dc.identifierhttp://arxiv.org/abs/math/0006211
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59493
dc.subjectQuantum Algebra
dc.subject17B37, 46L87, 81R50
dc.titleClassification of Left-Covariant Differential Calculi on the Quantum Group $\SLq 2$
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