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  • Artikel  (15)
  • 17B37  (15)
  • Springer  (15)
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  • Springer  (15)
  • American Chemical Society
  • American Chemical Society (ACS)
  • American Geophysical Union
  • Institute of Physics (IOP)
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  • 2015-2019
  • 1990-1994  (15)
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  • Physik  (15)
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  • Mathematik  (15)
  • 1
    Digitale Medien
    Digitale Medien
    Closed star products and cyclic cohomology (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 1-12 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 19P55 ; 17B37 ; 81S30 ; 19K56
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We define the notion of a closed star product. A (generalized) star product (deformation of the associative product of functions on a symplectic manifold W) is closed iff integration over W is a trace on the deformed algebra. We show that for these products the cyclic cohomology replaces the Hochschild cohomology in usual star products. We then define the character of a closed star product as the cohomology class (in the cyclic bicomplex) of a well-defined cocycle, and show that, in the case of pseudodifferential operators (standard ordering on the cotangent bundle to a compact Riemannian manifold), the character is defined and given by the Todd class, while in general it fails to satisfy the integrality condition.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00429997
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  • 2
    Digitale Medien
    Digitale Medien
    Quantum groups and diagonalization of the braid generator (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 183-196 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R10 ; 17B37 ; 16W30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract It is shown that the braid generator is diagonalizable on arbitrary tensor product modules V ⊗ V, V an irreducible module for a quantum group. A generalization of the Reshetikhin form for the braid generator is thereby obtained in the general case. As an application, a general closed formula is determined for link polynomials.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00402893
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  • 3
    Digitale Medien
    Digitale Medien
    Serre-type relations for special linear Lie superalgebras (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 173-181 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17A70 ; 16W30 ; 17B37 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract It is pointed out that, for m, n ≥2, the naive Serre presentation corresponding to the simplest Cartan matrix of sl(m, n) does not define the Lie superalgebra sl(m, n) but a larger algebra s(m, n) of which sl(m, n) is a nontrivial quotient. The supplementary relations for the generators are found and the definition of the q-deformed universal enveloping algebra of sl(m, n) is modified accordingly.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00402892
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  • 4
    Digitale Medien
    Digitale Medien
    Construction of a new quantum double and new solutions to the Yang-Baxter equation (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 197-203 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R10 ; 17B37 ; 16W30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract A new quantum double is established from a new Hopf algebra and a new kind of quantum R-matrix is obtained.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00402894
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  • 5
    Digitale Medien
    Digitale Medien
    Real forms of U q(g) (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 49-58 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16W30 ; 57T05 ; 17B37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract In this Letter we consider the real forms of quantum groups associated to generalized Cartan matrices. There are two main results. The first is a description of the Hopf algebra automorphisms and of the Hopf *-algebra structures of the quantum group. This immediately yields a precise description of the real forms. The second result establishes a correspondence of these real forms when the quantum group is associated to a complex simple Lie algebra with objects associated to the real forms of the classical object.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00430002
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  • 6
    Digitale Medien
    Digitale Medien
    The uniqueness theorem for the universal R-matrix (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 231-244 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R10 ; 17B37 ; 16W30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Up to now, the universal R-matrix for quantized Kac-Moody algebras Here the name \lsKac-Moody algebras\rs includes all semisimple finite-dimensional Lie algebras and all infinite-dimensional affine Kac-Moody algebras. is believed to be uniquely determined (for some ansatz) by properties of a quasi-cocommutativity and a quasi-triangularity. We prove here that the universal R-matrix (for the same ansatz) is uniquely determined by the property of the quasi-cocommutativity only. Thus, the quasi-triangular property (and the Yang-Baxter equation!) for the universal R-matrix is a consequence of the linear equation of the quasi-cocommutativity. The proof is based on properties of singular vectors in the tensor product of the Verma modules and the structure of extremal projector for quantized algebras. Explicit expressions of the universal R-matrix for quantized algebras U q (A inf1 sup(1) ) and U q (A inf2 sup(2) ) are given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00402899
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  • 7
    Digitale Medien
    Digitale Medien
    Star-products and phase space realizations of quantum groups (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 51-59 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 81R50 ; 81S30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00402375
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  • 8
    Digitale Medien
    Digitale Medien
    A natural and rigid model of quantum groups (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 75-84 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16W30 ; 81R50 ; 17B37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We introduce a natural (Fréchet-Hopf) algebra A containing all generic Jimbo algebras U t (sl(2)) (as dense subalgebras). The Hopf structures on A extend (in a continuous way) the Hopf structures of generic U t (sl(2)). The Universal R-matrices converge in A $$\hat \otimes $$ A. Using the (topological) dual of A, we recover the formalism of functions of noncommutative arguments. In addition, we show that all these Hopf structures on A are isomorphic (as bialgebras), and rigid in the category of bialgebras.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00402377
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  • 9
    Digitale Medien
    Digitale Medien
    A *-product on SL(2) and the corresponding nonstandard $$(\mathfrak{s}\mathfrak{l}({\text{2}}))$$ (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 85-88 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16W30 ; 17B37 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We obtain Zakrzewski's deformation of Fun SL(2) through the construction of a *-product on SL(2). We then give the deformation of $$(\mathfrak{s}\mathfrak{l}({\text{2}}))$$ dual to this, as well as a Poincaré basis for both algebras.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00398304
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  • 10
    Digitale Medien
    Digitale Medien
    Differential geometry on linear quantum groups (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 139-147 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract An exterior derivative, inner derivation, and Lie derivative are introduced on the quantum group GL q (N). SL q (N) is then found by constructing matrices with determnant unity, and the induced calculus is found.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00398310
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