Skip to main content
Article thumbnail
Location of Repository

Primitive ideals and automorphism group of Uq+(B2)

By Stephane Launois

Abstract

Let g be a complex simple Lie algebra of type B-2 and q be a nonzero complex number which is not a root of unity. In the classical case, a theorem of Dixmier asserts that the simple factor algebras of Gelfand-Kirillov dimension 2 of the positive part U+(g) of the enveloping algebra of g are isomorphic to the first Weyl algebra. In order to obtain some new quantized analogues of the first Weyl algebra, we explicitly describe the prime and primitive spectra of the positive part U+ q (g) of the quantized enveloping algebra of g and then we study the simple factor algebras of Gelfand-Kirillov dimension 2 of U+ q (g). In particular, we show that the centers of such simple factor algebras are reduced to the ground field C and we compute their group of invertible elements. These computations allow us to prove that the automorphism group of U-q(+) (g) is isomorphic to the torus (C*)(2), as conjectured by Andruskiewitsch and Dumas

Topics: QA
Publisher: World Scientific Publishing Company
Year: 2007
OAI identifier: oai:kar.kent.ac.uk:3155

Suggested articles

Citations

  1. (1974). Alg` ebres enveloppantes, Gauthier-Villars,
  2. (1974). Alge`bres enveloppantes, Gauthier-Villars,
  3. (1994). Automorphismes de Uq(b+),
  4. (1994). Automorphismes de Uq(b+), Beitra¨ge Algebra Geom.
  5. (1996). Catenarity in quantum algebras, doi
  6. (1995). Etude des q-commutations dans l’alg` ebre Uq(n+),
  7. (1995). Etude des q-commutations dans l’alge`bre Uq(n+), doi
  8. (1993). Generalized Weyl algebras and their representations, doi
  9. (2001). Isomorphism problems and groups of automorphisms for generalized Weyl algebras,
  10. Isomorphisms between quantum generalized Weyl algebras, ArXiv:math.QA/0402413, to appear in Journal of Algebra and its Applications. doi
  11. (1994). L’alg` ebre d’Heisenberg quantique,
  12. (1994). L’alge`bre d’Heisenberg quantique,
  13. (2002). Lectures on algebraic quantum groups, doi
  14. On the automorphisms of U+ doi
  15. On the automorphisms of U+q doi
  16. (1996). PBW-bases of quantum groups, doi
  17. (1994). Prime factor algebras of the coordinate ring of quantum matrices, doi
  18. (1990). Q-analogs of Clifford and Weyl algebras - Spinor and oscillator representation of quantum enveloping algebras, doi
  19. (1993). q-analogs of harmonic oscillators and related rings, doi
  20. (1996). Rigidit´ e des plongements des quotients primitifs minimaux de Uq(sl(2)) dans l’alg` ebre quantique de Weyl-Hayashi,
  21. (1996). Rigidite´ des plongements des quotients primitifs minimaux de Uq(sl(2)) dans l’alge`bre quantique de Weyl-Hayashi,
  22. (1986). Un automorphisme non mod´ er´ e de doi
  23. (1986). Un automorphisme non mode´re´ de U(g3), doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.