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  • Articles  (23)
  • 81R50  (23)
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  • Articles  (23)
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  • Springer  (23)
  • American Meteorological Society
  • American Physical Society (APS)
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  • 1
    Electronic Resource
    Electronic Resource
    q-Difference intertwining operators and q-conformal invariant equations (1996)
    Springer
    Acta applicandae mathematicae 44 (1996), S. 81-116 
    Details
    ISSN: 1572-9036
    Keywords: 17B37 ; 81R50 ; 22E47 ; quantum groups ; intertwining differential operators ; conformal invariance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We first recall a canonical procedure for the construction of the invariant differential operators and equations for arbitrary complex or real noncompact semisimple Lie groups. Then we present the application of this procedure to the case of quantum groups. In detail is given the construction of representations of the quantum algebra U q (sl(n)) labelled by n−1 complex numbers and acting in the spaces of functions of n(n−1)/2 noncommuting variables, which generate a q-deformed SL(4) flag manifold. The conditions for reducibility of these representations and the procedure for the construction of the q-difference intertwining operators are given. Using these results for the case n=4 we propose infinite hierarchies of q-difference equations which are q-conformal invariant. The lowest member of one of these hierarchies are new q-Maxwell equations. We propose also new q-Minkowski spacetime which is part of a q-deformed SU(2,2) flag manifold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00116517
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  • 2
    Electronic Resource
    Electronic Resource
    Multiparameter quantum function algebra at roots of 1 (1996)
    Springer
    Mathematische Annalen 306 (1996), S. 759-780 
    Details
    ISSN: 1432-1807
    Keywords: 16W30 ; 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01445276
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  • 3
    Electronic Resource
    Electronic Resource
    Gauss laws in the sense of Bernstein and uniqueness of embedding into convolution semigroups on quantum groups and braided groups (1997)
    Springer
    Probability theory and related fields 109 (1997), S. 101-127 
    Details
    ISSN: 1432-2064
    Keywords: Mathematics Subject Classification (1991): 60B99 ; 16W30 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. The goal of this paper is to characterise certain probability laws on a class of quantum groups or braided groups that we will call nilpotent. First we introduce a braided analogue of the Heisenberg–Weyl group, which shall serve as standard example. We introduce Gaussian functionals on quantum groups or braided groups as functionals that satisfy an analogue of the Bernstein property, i.e. that the sum and difference of independent random variables are also independent. The corresponding functionals on the braided line, braided plane and a braided q-Heisenberg–Weyl group are determined. Section 5 deals with continuous convolution semigroups on nilpotent quantum groups and braided groups. We extend recent results proving the uniqueness of the embedding of an infinitely divisible probability law into a continuous convolution semigroup for simply connected nilpotent Lie groups to nilpotent quantum groups and braided groups. Finally, in Section 6 we give some indications how the semigroup approach of Heyer and Hazod to the Bernstein theorem on groups can be extended to quantum groups and braided groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004400050127
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  • 4
    Electronic Resource
    Electronic Resource
    q-Gravity (1996)
    Springer
    Letters in mathematical physics 38 (1996), S. 53-62 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 81V17 ; quantum groups ; gravitation ; Lorentz groups
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Since general relativity may be regarded as a non-Abelian gauge theory obtained by gauging the Lorentz group, one may obtain its q-deformation by gauging the q-Lorentz group. The q-dependent action resulting from this construction describes interacting gravitational and spinor fields. This action is invariant under nonlocal q-transformations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398298
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  • 5
    Electronic Resource
    Electronic Resource
    The quantum Sturm-Liouville equation, quantum resolvent, quantum integrals, and quantum KdV: The fast decrease case (1996)
    Springer
    Letters in mathematical physics 36 (1996), S. 427-439 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 81Q15 ; 81T40 ; 81U40 ; 35Q53 ; 35K22 ; 35P25 ; 35Q15 ; Sturm-Liouville equation ; nonlinear Fourier transform ; quantum resolvent equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum field O(k) and the regularization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00714407
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  • 6
    Electronic Resource
    Electronic Resource
    A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions (1996)
    Springer
    Letters in mathematical physics 38 (1996), S. 33-51 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 17B65 ; 81R50 ; quantum deformation ; Virasoro algebra ; bosonic realization ; Macdonald symmetric functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra. Singular vectors are expressed by the Macdonald symmetric functions. This is proved by constructing screening currents acting on the bosonic Fock space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398297
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  • 7
    Electronic Resource
    Electronic Resource
    Schrödinger equations for su q (2)-invariant quantum systems (1996)
    Springer
    Letters in mathematical physics 36 (1996), S. 169-176 
    Details
    ISSN: 1573-0530
    Keywords: 81R20 ; 81R50 ; quantum groups ; quantum algebras ; Schrödinger equations ; Hamiltonians ; Coulomb potential
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract By deforming the Hamiltonian of a spinless particle in a central potential we set up su q (2)-invariant Schrödinger equations within the usual framework of quantum mechanics. Different deformations correspond to a given Hamiltonian. We explicitly solve different stationary Schrödinger equations for the free particle and for the hydrogen atom, and compare the associated energy spectra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00714379
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  • 8
    Electronic Resource
    Electronic Resource
    R-matrix formulation of the quantum inhomogeneous groups ISO q,r (N) and ISp q,r (N) (1996)
    Springer
    Letters in mathematical physics 36 (1996), S. 197-211 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 22E70 ; Multi parametric quantum inhomogeneous groups ; quantum Poincaré groups ; quotient Hopf algebras
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The quantum commutationsRTT=TTR and the orthogonal (symplectic) conditions for the inhomogeneous multiparametricq-groups of theB n ,C n ,D n type are found in terms of theR-matrix ofB n+1 ,C n+1 ,D n+1 .A consistent Hopf structure on these inhomogeneousq-groups is constructed by means of a projection fromB n+1 ,C n+1 ,D n+1 .Real forms are discussed; in particular, we obtain theq-groups ISO q,r (n+1,n−1), including the quantum Poincaré group. The inhomogeneusq-groups do not contain dilatations when the parameters satisfy certain conditions. For example, we find a dilatation-freeq-Poincaré group depending on one real parameterq.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00714382
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  • 9
    Electronic Resource
    Electronic Resource
    Real forms of the oscillator quantum algebra and its representations (1996)
    Springer
    Letters in mathematical physics 36 (1996), S. 77-85 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 22E70 ; oscillator quantum algebra ; Hopf algebras ; real forms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the conditions under which the q-oscillator algebra becomes a Hopf *-algebra. In particular, we show that there are at least two real forms associated with the algebra. Furthermore, through the representations, it is shown that they are related to su q1/2(2) with different conjugations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00403253
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  • 10
    Electronic Resource
    Electronic Resource
    Operator representations of U q (sl2(ℝ)) (1996)
    Springer
    Letters in mathematical physics 37 (1996), S. 211-222 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 47D40 ; star algebra ; Hopf algebra ; operator representations ; Casimir operators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Integrable (‘well-behaved’) operator representations of the *-algebra U q (sl2(ℝ)), |q|= 1, q 2 ≠ 1, |q|=1, q2 ≠ 1, in Hilbert space are defined and classified up to unitary equivalence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00416024
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