✦ LIBER ✦
Classification of Left-Covariant Differential Calculi on the Quantum Group SLq(2)
✍ Scribed by István Heckenberger
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 245 KB
- Volume
- 237
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
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 SL q 2 are given. All such differential calculi 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 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.