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  • Articles  (14)
  • 16W30  (14)
  • Springer  (14)
  • Blackwell Publishing Ltd
  • Elsevier
  • 2020-2022
  • 2000-2004
  • 1990-1994  (14)
  • 2004
  • 1992  (14)
  • Mathematics  (14)
  • Natural Sciences in General
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  • Articles  (14)
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  • Springer  (14)
  • Blackwell Publishing Ltd
  • Elsevier
Years
  • 2020-2022
  • 2000-2004
  • 1990-1994  (14)
Year
Topic
  • Mathematics  (14)
  • Natural Sciences in General
  • Physics  (14)
  • 1
    Electronic Resource
    Electronic Resource
    Differential operators on quantum spaces for GL q (n) and SO q (n) (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 245-255 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 81R05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove that the rings of q-differential operators on quantum planes of the GL q (n) and SO q (n) types are isomorphic to the rings of classical differential operators. Also, we construct decompositions of the rings of q-differential operators into tensor products of the rings of q-differential operators with less variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402900
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  • 2
    Electronic Resource
    Electronic Resource
    Quantum groups and diagonalization of the braid generator (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 183-196 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402893
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  • 3
    Electronic Resource
    Electronic Resource
    Serre-type relations for special linear Lie superalgebras (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 173-181 
    Details
    ISSN: 1573-0530
    Keywords: 17A70 ; 16W30 ; 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402892
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  • 4
    Electronic Resource
    Electronic Resource
    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
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A new quantum double is established from a new Hopf algebra and a new kind of quantum R-matrix is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402894
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  • 5
    Electronic Resource
    Electronic Resource
    Real forms of U q(g) (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 49-58 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 57T05 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00430002
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  • 6
    Electronic Resource
    Electronic Resource
    The uniqueness theorem for the universal R-matrix (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 231-244 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402899
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  • 7
    Electronic Resource
    Electronic Resource
    A natural and rigid model of quantum groups (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 75-84 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 81R50 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402377
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  • 8
    Electronic Resource
    Electronic Resource
    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
    Keywords: 16W30 ; 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398304
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  • 9
    Electronic Resource
    Electronic Resource
    Rational forms for twistings of enveloping algebras of simple Lie algebras (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 111-120 
    Details
    ISSN: 1573-0530
    Keywords: 17B20 ; 16S35 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give ‘rational’ forms for twistings of classical enveloping algebras. We also remark a link with the ‘generalized formalism’ of Gurevich, Manin, and Cartier.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398307
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  • 10
    Electronic Resource
    Electronic Resource
    Reality in the differential calculus on q-Euclidean spaces (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 121-130 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 81R05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The nonlinear reality structure of the derivatives and the differentials for the Euclidean q-spaces are found. A real Laplacian is constructed and reality properties of the exterior derivative are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398308
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