1. Le langage des espaces et des groupes quantiques
- Author
-
Georges Maltsiniotis
- Subjects
58B30 ,Quantum geometry ,Pure mathematics ,Group (mathematics) ,Quantum group ,46L87 ,Statistical and Nonlinear Physics ,Differential calculus ,Quantum spacetime ,Automorphism ,17B37 ,Algebra ,Hyperplane ,Quantum ,Mathematical Physics ,Mathematics - 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.
- Published
- 1993