2000/06/28 by I. Heckenberger, Heckenberger, I.
Mathematics · #17B37 #46L87 #81R50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:46L87 #msc:81R50
paper · pdf · doi:10.48550/arxiv.math/0006211
LaTeX2e, 43 pages, to appear in Journal of Algebra
arxiv created 2000/06/28 · openalex publication_date 2000/06/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(u12), ω(u21) and ω(u11-u22) 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