Letters in Mathematical Physics

, Volume 36, Issue 2, pp 109–116 | Cite as

Deformations of quantum hyperplanes

  • Gerhard Post


We consider the quantum hyperplanex i x j =q ij x j x i (i,j = 1..n) and define and consider deformations of the formx i x j =q ij x j x i + Σ k α k ij x k + β ij , where α k ij and β ij are complex numbers. We prove that for genericq ij no nontrivial deformations exist forn ≥ 3.

Mathematics Subject Classifications (1991)

17B37 16E40 

Key words

quantum hyperplanes PBW theorem deformations cohomology 


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  1. 1.
    BahhturinY. A., MikhalevA. A., PetrogradskyV. M. and ZaicevM. V.,Infinite Dimensional Lie Algebras, Walter de Gruyter, Berlin, 1992.Google Scholar
  2. 2.
    GerstenhaberM. and ShackS. D., Algebraic cohomology and deformation theory, inDeformation Theory of Algebras and Structure and Application, NATO ASI series C-Vol. 247, Kluwer, Dordrecht, 1992.Google Scholar
  3. 3.
    BergmanG. M., The diamond lemma for ring theory,Adv. Math. 29 (1978), 178–218.Google Scholar
  4. 4.
    Braverman, A. and Gaitsgory, D., Poincaré-Birkhoff-Witt theorem for quadratic algebras of Koszul type, Preprint hep-th/9411113.Google Scholar
  5. 5.
    NijenhuisA. and RichardsonR. W., Deformations of Lie algebra structures,J. Math. Mech. 17 (1967), 89–105.Google Scholar
  6. 6.
    WittenE., Gauge theories, vector models and quantum groups,Nuclear Phys. B 330 (1990), 285–346.Google Scholar
  7. 7.
    FairlyD., Quantum deformations of SU(2),J. Phys. A 23 (1990), 183–187.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Gerhard Post
    • 1
  1. 1.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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