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Classification of three-dimensional covariant differential calculi on Podles' quantum spheres and on related spaces (1994)

Apel, Joachim ; Schmüdgen, Konrad

Springer

Letters in mathematical physics 32 (1994), S. 25-36

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ISSN: 1573-0530

Keywords: 17B37 ; 46L87 ; 81R50

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract Covariant differential calculi on the quantum space $$\mathfrak{X}_{q\lambda \rho }$$ for the quantum group SL q (2) are classified. Our main assumptions are thatq is not a root of unity and that the differentials de j of the generators of $$\mathfrak{X}_{q\lambda \rho }$$ form a free right module basis for the first-order forms. Our result says, in particular, that apart from the two casesc =c(3), ∞ there exists a unique differential calculus with the above properties on the space $$\mathfrak{X}_{q\lambda \rho }$$ which corresponds to Podles' quantum sphereS qc /2 .

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00761121

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