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Algebras symmetries spaces

  • V. Non-commutative Geometry
  • Conference paper
  • First Online:
Quantum Groups

Part of the book series: Lecture Notes in Physics ((LNP,volume 370))

  • 149 Accesses

Abstract

After discussing several aspects of non-commutative geometry from a rather subjective point of view, algebraic techniques are shown to offer a powerful tool for studying specific manifolds in the realm of commutative geometry, with possible generalization to infinite dimensions.

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References

  1. A. Jadczyk and D. Kastler. Lie-cartan pairs I. Rep.Math.Phys, 25:1–51, 1987.

    Google Scholar 

  2. A. Jadczyk and D. Kastler. Lie-cartan pairs II. Ann. Phys, 179:169–200, 1987.

    Google Scholar 

  3. R. Coquereaux, A. Jadczyk, and D. Kastler. Differential and integral geometry of grassmann algebras, to appear.

    Google Scholar 

  4. W. Marcinek. Generalized Lie Algebras I,II Rep.Math.Phys, 1988.

    Google Scholar 

  5. U. Bannier. Allgemeine kovariante algebraische Quantenfeldtheorie und Rekonstruktion von Raum-Zeit. PhD thesis, University Hamburg, 1987.

    Google Scholar 

  6. H.D. Doebner and W. Lücke. Quantum logic as a consequence of realistic measurements on deterministic systems, to appear in J.Math.Phys..

    Google Scholar 

  7. B. Mielnik. Theory of filters.. Commun. math. Phys, 15:1–46, 1969.

    Google Scholar 

  8. H. Araki. On a characterization of the state space of quantum mechanics. Commun. math. Phys, 75:1–24, 1980.

    Google Scholar 

  9. C. Piron. New quantum mechanics. In Essays in Honour of W. Yourgrau, Plenum N.Y., 1983 pp. 345–361.

    Google Scholar 

  10. N. Giovannini. Classical and quantal systems of imprimitivity. J.Math.Phys., 22:2389–2403, 1981.

    Google Scholar 

  11. F. Reusse. On classical and quantum relativistic dynamics. Found.Phys., 9:865–882, 1979.

    Google Scholar 

  12. B. Mielnik. Generalized quantum mechanics. Commun.math. Phys., 37:221–256, 1974

    Google Scholar 

  13. R. Haag and U. Barmier. Comments on Mielnik's generalized (non linear) quantum mechanics. Commun.math. Phys., 60:1–6, 1975.

    Google Scholar 

  14. A. Odzijewicz. On reproducing kernels and quantization of states. Commun.math.Phys., 114:577–597,1988.

    Google Scholar 

  15. I.T. Todorov. Conformal Description of Spinning Particles. Springer Verlag, Berlin-Heidelberg, 1986.

    Google Scholar 

  16. G.J. Zuckerman. Quantum physics and semisimple symmetric spaces. in Lect. Notes Math., 1077, 1984

    Google Scholar 

  17. A. Jadczyk. Geometry of indefinite metric spaces. Rep.Math.Phys, 1:263–276, 1971.

    Google Scholar 

  18. R. Coquereaux. Non-commutative geometry and theoretical physics. (Preprint).

    Google Scholar 

  19. R. Coquereaux and A. Jadczyk. Conformal theories, curved phase spaces, relativistic wavelets and the geometry of complex domains Preprint CPT89/ P.2302 Marseille

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wrocław, Cybulskiego 36, 50 205, Wrocław, Poland

    A. Jadczyk

Authors
  1. A. Jadczyk
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Editor information

H. -D. Doebner J. -D. Hennig

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© 1990 Springer-Verlag

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Jadczyk, A. (1990). Algebras symmetries spaces. In: Doebner, H.D., Hennig, J.D. (eds) Quantum Groups. Lecture Notes in Physics, vol 370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53503-9_57

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  • DOI: https://doi.org/10.1007/3-540-53503-9_57

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53503-4

  • Online ISBN: 978-3-540-46647-5

  • eBook Packages: Springer Book Archive

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