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Le langage des espaces et des groupes quantiques

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Abstract

We study the foundations of the differential calculus in quantum geometry. The notions of (differential) quantum space and cone are introduced. Generalizing a construction of Manin, to a quantum cone we associate the quantum group of its “linear automorphisms preserving the differentials” and deduce a de Rham complex on this group. We give examples of differential calculi on quantum hyperplanes and quantum linear groups.

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Authors and Affiliations

  1. UFR de Mathématiques, Université de Paris VII, Tours 45-55 5ème étage, 2, Place Jussieu, F-75251, Paris Cedex 05, France

    Georges Maltsiniotis

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  1. Georges Maltsiniotis
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Communicated by K. Gawedzki

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Maltsiniotis, G. Le langage des espaces et des groupes quantiques. Commun.Math. Phys. 151, 275–302 (1993). https://doi.org/10.1007/BF02096770

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  • DOI: https://doi.org/10.1007/BF02096770

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