Géométrie de l'espace tangent sur l'hyperboloïde quantique

P. Akueson

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2001)

  • Volume: 42, Issue: 1, page 2-50
  • ISSN: 1245-530X

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Akueson, P.. "Géométrie de l'espace tangent sur l'hyperboloïde quantique." Cahiers de Topologie et Géométrie Différentielle Catégoriques 42.1 (2001): 2-50. <http://eudml.org/doc/91640>.

@article{Akueson2001,
author = {Akueson, P.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {quantum hyperboloid; braided geometry; quantum group; tangent space of quantum hyperboloid},
language = {fre},
number = {1},
pages = {2-50},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Géométrie de l'espace tangent sur l'hyperboloïde quantique},
url = {http://eudml.org/doc/91640},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Akueson, P.
TI - Géométrie de l'espace tangent sur l'hyperboloïde quantique
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2001
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 42
IS - 1
SP - 2
EP - 50
LA - fre
KW - quantum hyperboloid; braided geometry; quantum group; tangent space of quantum hyperboloid
UR - http://eudml.org/doc/91640
ER -

References

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  1. [A] P. Akueson: Éléments de Géométrie tressée, Thèse de l'Université de Valenciennes (1998). 
  2. [AG] P. Akueson, D. Gurevich: Some aspects of braided geometry : differential calculus, tangent space, gauge theory, to appear in J.Phys.A., (1999). Zbl0945.58007MR1696901
  3. [BM] T. Brzezinski, S. Majid:Line bundles on quantum sphere, q-alg/9807052. 
  4. [DGK] J. Donin, D. Gurevich, S. Khoroshkin: Double quantization of CPn type orbits by generalized Verma modules, JGP,28 (1998) pp.384-406. Zbl0945.17003MR1658719
  5. [DGS] J. Donin, D. Gurevich, S. Shnider: Invariant quantization in one and two parameters on semisimple coadjoint orbits of simple Lie groups, J. Pure and App. Algebra100 (1995), pp.103-115. MR1344846
  6. [DGR] J. Donin, D. Gurevich, V. Rubtsov: Quantum hyperboloid and braided modules, Algèbre Non Commutative, Groupes quantiques et invariants, Société Mathématique de France, Collection séminaires et congrès, No 2 (1997), pp.103-118. Zbl0973.17502MR1601123
  7. [D] J. Donin: Double quantization on the coadjoint representation of sl(n), Czech J.of Physics, 47, (1997), pp. 1115-1122. Zbl0942.17006MR1615893
  8. [FRT] L. Faddeev, N. Reshetikhin, L. Takhtadhyan: Quantization of Lie groups and Lie algebras, Leningrad Math.J.1 (1990), pp.193-226. Zbl0715.17015MR1015339
  9. [GRR] D. Gurevich, A. Radul, V. Rubtsov: Noncommutative differential geometry and Yang-Baxter equation, Preprint. Publ. Math. IHES (1991). 
  10. [GP] D. Gurevich, D. Panyushev: On Poisson pairs associated to modified R-matrices, Duke Math.J.73 (1994), no.1. Zbl0824.58022MR1262206
  11. [DG] D. Gurevich, J. Donin: Braiding of the Lie algebra sl(2), Amer.Math.Soc.Transl.(2) 167 (1995), pp.23-36. Zbl0853.17009MR1343982
  12. [GV] D. Gurevich, L. Vainerman: Noncommutative analogues of q-special polynomials and a q-integral on a sphere, J.Phys.A. Math.Gen.31 (1998), pp.1771-1780. Zbl0904.33014MR1624601
  13. [G1] D. Gurevich: Algebraic aspects of the quantum Yang-Baxter equation, Leningrad. Math.J.2 (1991), pp. 801-828. Zbl0728.17012MR1080202
  14. [G2] D. Gurevich: Braided modules and reflection equations, Quantum groups and quantum spaces. Banach Center Publ, (40), Institut of Math, Polish Academy of Sciences, Warszawa1997, pp.99-109. Zbl0936.17014MR1481738
  15. [K] C. Kassel: Quantum groups, Graduate texts in mathematics, 155, (1995). Zbl0808.17003MR1321145
  16. [L] J. Lambek: Lectures on rings and modules, Blaisddell publishing company (1966). Zbl0143.26403MR419493
  17. [LS] V. Lyubashenko, A. Sudbery: Quantum Lie algebras of type An, q-alg /9510004. 
  18. [M] Sh. Majid: Foundations of quantum groups theory, Cambrige University Press, (1995). Zbl0857.17009MR1381692
  19. [P] P. Podlès: Quantum spheres, Lett.Math.Phys.14 (1987), pp.193-202. Zbl0634.46054MR919322
  20. [R] G. Rinehart: Differential forms for general commutative algebras, Trans.Amer.Math.Soc.108 (1963), pp.195-222. Zbl0113.26204MR154906
  21. [S1] J.P. Serre: Modules projectifs et espaces fibrés a fibre vectorielle, exp. 23, Séminaire Dubreil-Pisot, Algèbre et théorie des nombres, Secrétariat mathématique, Paris, 1958. Zbl0132.41202MR177011
  22. [S2] A. Sudbery: SUq(n) gauge theory, Phys.Letters B375 (1996), pp. 75-80. Zbl0997.81531MR1396485

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