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  • 1
    Electronic Resource
    Electronic Resource
    On the defining relations of quantum superalgebras (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 127-131 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 16S80 ; 22E70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In defining quantum superalgebras, extra relations need to be added to the Serre-like relations. They are obtained for sl q (m, n) and osp q (m, 2n) usingq-oscillator representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00703725
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  • 2
    Electronic Resource
    Electronic Resource
    Six generatorq-deformed Lorentz algebra (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 233-240 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 81R05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The six generator deformation of the Lorentz algebra is presented. The Hopf algebra structure and the reality conditions are found. The chiral decomposition of SL(2, C) is generalized to theq-case. Casimir operators for theq-Lorentz algebra are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01885501
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  • 3
    Electronic Resource
    Electronic Resource
    On the universalR-matrix for Uq(241-1241-1241-1) (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 241-250 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 17B37 ; 16W30 ; 81R30 ; 81S05 ; 81T40 ; 20F36
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A compact form for the universalR-matrix of U q (sl n ) is derived and illustrated by simple applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01885502
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  • 4
    Electronic Resource
    Electronic Resource
    Singular vectors of quantum group representations for straight Lie algebra roots (1991)
    Springer
    Letters in mathematical physics 22 (1991), S. 251-266 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give explicit formulae for singular vectors of Verma modules over Uq(G), where G is any complex simple Lie algebra. The vectors we present correspond exhaustively to a class of positive roots of G which we call straight roots. In some special cases, we give singular vectors corresponding to arbitrary positive roots. For our vectors we use a special basis of Uq(G -), where G - is the negative roots subalgebra of G, which was introducted in our earlier work in the case q=1. This basis seems more economical than the Poincaré-Birkhoff-Witt type of basis used by Malikov, Feigin, and Fuchs for the construction of singular vectors of Verma modules in the case q=1. Furthermore, this basis turns out to be part of a general basis recently introduced for other reasons by Lusztig for Uq(ℬ-), where ℬ- is a Borel subalgebra of G.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00405600
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  • 5
    Electronic Resource
    Electronic Resource
    Differential calculi on quantum vector spaces with Hecke-type relations (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 133-141 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16O80 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract From a vector spaceV equipped with a Yang-Baxter operatorR one may form the r-symmetric algebraS R V=TV/〈v ⊗w−R(v ⊗w)〉, which is a quantum vector space in the sense of Manin, and the associated quantum matrix algebraM R V=T(End(V))/〈f ⊗g−R(f ⊗g)R -1〉. In the case whenR satisfies a Hecke-type identityR 2=(1−q)R+q, we construct a differential calculus Ω R V forS R V which agrees with that constructed by Pusz, Woronowicz, Wess, and Zumino whenR is essentially theR-matrix of GL q (n). Elements of Ω R V may be regarded as differential forms on the quantum vector spaceS R V. We show that Ω R V isM R V-covariant in the sense that there is a coaction Φ*: Ω R V →M R V ⊗ Ω R V with Φ*d=(1 ⊗ d)Φ* extending the natural coaction Φ:S R V →M R V ⊗S R V.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00703726
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  • 6
    Electronic Resource
    Electronic Resource
    Braided groups and algebraic quantum field theories (1991)
    Springer
    Letters in mathematical physics 22 (1991), S. 167-175 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 18D10 ; 20N99 ; 81T05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We introduce the notion of a braided group. This is analogous to a supergroup with Bose-Fermi statistics ±1 replaced by braid statistics. We show that every algebraic quantum field theory in two dimensions leads to a braided group of internal symmetries. Every quantum group can be viewed as a braided group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00403542
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  • 7
    Electronic Resource
    Electronic Resource
    Orbifolds, Hopf algebras, and the Moonshine (1991)
    Springer
    Letters in mathematical physics 22 (1991), S. 187-194 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We describe the modular properties and fusion rules of holomorphic orbifold models by Hopf algebraic techniques, using the representation theory of the orbifold quantum group. We apply this theory to the construction of generalized Thompson series, and discuss its connections with Moonshine.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00403544
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  • 8
    Electronic Resource
    Electronic Resource
    An algebra related to the fusion rules of Wess-Zumino-Witten models (1991)
    Springer
    Letters in mathematical physics 22 (1991), S. 291-296 
    Details
    ISSN: 1573-0530
    Keywords: 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We introduce a new family of examples of ‘quantum groups’. Its irreducible representations are indexed by level l dominant integral weights of affine Lie algebra sī(n), and their branching rules with respect to the ‘truncated tensor product’ $$\bar\otimes $$ is given by the fusion rules of SU(n) l -Wess-Zumino-Witten model in conformal field theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00405604
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  • 9
    Electronic Resource
    Electronic Resource
    Fusion rule engineering (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 11-18 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 16Dxx ; 81T
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The determination of the fusion rules of WZW theories constitutes an important step in the program of classifying and solving conformal field theories. A drawback of the existing algorithms for such calculations is that, even at a modestly large number of primary fields, they require an enormous amount of computer time and memory. However, by breeding together two of these algorithms in an appropriate manner, it is possible to speed up the calculations and, therefore, greatly extend the accessible range of theories.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01811289
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  • 10
    Electronic Resource
    Electronic Resource
    Solutions of the braid equation related to a Hopf algebra (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 143-145 
    Details
    ISSN: 1573-0530
    Keywords: 57T05 ; 16W30 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Two solutionsT andT′ of the braid equation acting onA ⊗A (whereA is a Hopf algebra) are described. IfA is a cocommutative, thenT=σ. IfA is commutative, thenT′=σ (σ denotes the flip: σ(a ⊗b) =b ⊗a for anya,b ∈A).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00703727
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