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  • 16W30  (1)
  • 83E30  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 156 (1993), S. 581-605 
    ISSN: 1432-0916
    Keywords: Quantum group ; primitive ideal ; Poisson Lie group ; symplectic leaves ; 17B37 ; 16W30 ; 16S80 ; 16S30 ; 58F06 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The primitive ideals of the Hopf algebraC q [SL(3)] are classified. In particular it is shown that the orbits in PrimC q [SL(3)] under the action of the representation groupH ≅C *×C * are parameterized naturally byW×W, whereW is the associated Weyl group. It is shown that there is a natural one-to-one correspondence between primitive ideals ofC q [SL(3)] and symplectic leaves of the associated Poisson algebraic groupSL(3,C).
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 172 (1995), S. 571-622 
    ISSN: 1432-0916
    Keywords: 17B67 ; 17B81 ; 81R10 ; 83E30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An attempt is made to understand the root spaces of Kac Moody algebras of hyperbolic type, and in particularE 10, in terms of a DDF construction appropriate to a subcritical compactified bosonic string. While the level-one root spaces can be completely characterized in terms of transversal DDF states (the level-zero elements just span the affine subalgebra), longitudinal DDF states are shown to appear beyond level one. In contrast to previous treatments of such algebras, we find it necessary to make use of a rational extension of the self-dual root lattice as an auxiliary device, and to admit non-summable operators (in the sense of the vertex algebra formalism). We demonstrate the utility of the method by completely analyzing a non-trivial level-two root space, obtaining an explicit and comparatively simple representation for it. We also emphasize the occurrence of several Virasoro algebras, whose interrelation is expected to be crucial for a better understanding of the complete structure of the Kac Moody algebra.
    Type of Medium: Electronic Resource
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