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  • Articles  (12)
  • 17B37  (12)
  • Springer  (12)
  • American Geophysical Union (AGU)
  • Annual Reviews
  • 1995-1999  (12)
  • 1980-1984
  • 1935-1939
  • 1995  (12)
  • Mathematics  (12)
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  • Articles  (12)
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  • Springer  (12)
  • American Geophysical Union (AGU)
  • Annual Reviews
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  • 1995-1999  (12)
  • 1980-1984
  • 1935-1939
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  • 1
    Electronic Resource
    Electronic Resource
    Braided Hopf algebras and differential calculus (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 33-38 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show that the algebra of the bicovariant differential calculus on a quantum group can be understood as a projection of the cross-product between a braided Hopf algebra and the quantum double of the quantum group. The resulting super-Hopf algebra can be reproduced by extending the exterior derivative to tensor products.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750809
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  • 2
    Electronic Resource
    Electronic Resource
    Integration over the group space of SUq(2), Clebsch-Gordan coefficients, and related identities (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 221-229 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We calculate the Clebsch-Gordan coefficients of SUq(2) by a Woronowicz integration over the group manifold and obtain a representation differing from that reached by working with theq-group algebra. These apparently different results must agree, however, and their equivalence implies aq-identity. On lettingq = 1, we shall obtain two results of different structures for the Clebsch-Gordan coefficients of SU(2) and their equivalence similarly implies an identity among the usual binomial coefficients. With the same approach, one may extend the Woronowicz integral of the product of two irreducible representations to products of many irreducible representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749623
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  • 3
    Electronic Resource
    Electronic Resource
    Quantum orbits of theR-matrix type (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 263-276 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Given a simple Lie algebra g, we consider the orbits in g* which are of theR-matrix type, i.e., which possess a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the so-calledR-matrix bracket. We call an algebra quantizing the latter bracket a quantum orbit of theR-matrix type. We describe some orbits of this type explicitly and we construct a quantization of the whole Poisson pencil on these orbits in a similar way. The notions ofq-deformed Lie brackets, braided coadjoint vector fields, and tangent vector fields are discussed as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00761298
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  • 4
    Electronic Resource
    Electronic Resource
    Cohomology and deformation of Leibniz pairs (1995)
    Springer
    Letters in mathematical physics 34 (1995), S. 77-90 
    Details
    ISSN: 1573-0530
    Keywords: 16E40 ; 16W30 ; 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebraA together with a Lie algebraL mapped into the derivations ofA. A bicomplex (with both Hochschild and Chevalley-Eilenberg cohomologies) is essential.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739377
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  • 5
    Electronic Resource
    Electronic Resource
    BRST structures and symplectic geometry on a class of supermanifolds (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 207-219 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 17B37 ; 58A50 ; 81Q60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract By investigating the symplectic geometry and geometric quantization of a class of supermanifolds, we exhibit BRST structures for a certain kind of algebras. We discuss the undeformed andq-deformed cases in the classical as well as in the quantum cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749622
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  • 6
    Electronic Resource
    Electronic Resource
    Noncommutative symmetric functions and laplace operators for classical Lie algebras (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 135-143 
    Details
    ISSN: 1573-0530
    Keywords: 17B35 ; 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some properties of the noncommutative symmetric functions associated with a matrix. The decomposition of the Sklyanin determinant into a product of quasi-determinants play the main role in the construction. Analogous decomposition for the quantum determinant provides an alternative proof of the known construction for the Lie algebra gl(N).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750763
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  • 7
    Electronic Resource
    Electronic Resource
    Quantum algebras for maximal motion groups ofN-dimensional flat spaces (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 273-281 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An embedding method to getq-deformations for the nonsemisimple algebras generating the motion groups ofN-dimensional flat spaces is presented. This method gives a global and simultaneous scheme ofq-deformation for all iso(p, q) algebras and for those obtained from them by some Inönü-Wigner contractions, such as theN-dimensional Euclidean, Poincaré, and Galilei algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749681
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  • 8
    Electronic Resource
    Electronic Resource
    A quantum dual pair $$\mathfrak{s}\mathfrak{l}_2 ,\mathfrak{o}_n $$ and the associated Capelli identity (1995)
    Springer
    Letters in mathematical physics 34 (1995), S. 1-8 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A quantum analogue of the dual pair $$\mathfrak{s}\mathfrak{l}_2 ,\mathfrak{o}_n $$ is introduced in terms of the oscillator representation of U q $$(\mathfrak{s}\mathfrak{l}_2 )$$ . Its commutant and the associated identity of Capelli type are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739369
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  • 9
    Electronic Resource
    Electronic Resource
    Coherent states of theq-Weyl algebra (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 179-185 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 33D80 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract New coherent states of theq-Weyl algebraAA † −qA † A = 1,0 〈q 〈 1, are constructed. They are defined as eigenstates of the operatorA † which is the lowering operator for nonhighest weight representations describing positive energy states. Depending on whether the positive spectrum is discrete or continuous, these coherent states are related either to the bilateral basic hypergeometric series or to some integrals over them. The free particle realization of theq-Weyl algebra whenA † A ∞ d2/dx2 is used for illustrations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750767
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  • 10
    Electronic Resource
    Electronic Resource
    Linear connections on the quantum plane (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 351-358 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 53B05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750842
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  • 11
    Electronic Resource
    Electronic Resource
    The quantum super-Yangian and Casimir operators of Uq(gl(M |N)) (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 263-272 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 17A70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract TheZ 2 graded Yangian Yq(gl(M |N)) associated with the Perk-SchultzR matrix is introduced. Its structural properties, the central algebra in particular, are studied. AZ 2-graded associative algebra epimorphism Yq(gl(M |N)) → Uq (gl(M |N)) is obtained in explicit form. Images of central elements of the quantum super-Yangian under this epimorphism yield the Casimir operators of the quantum supergroup Uq(gl(M |N)) constructed in an earlier publication.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749628
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  • 12
    Electronic Resource
    Electronic Resource
    Minimal affinizations of representations of quantum groups: The nonsimply-laced case (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 99-114 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 17B65
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract If U q (g) is a finite-dimensional complex simple Lie algebra, an affinization of a finite-dimensional irreducible representationV of U q (g) is a finite-dimensional irreducible representation $$\hat V$$ of U q (ĝ) which containsV with multiplicity one, and is such that all other U q (g)-types in $$\hat V$$ have highest weights strictly smaller than that ofV. There is a natural partial ordering $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \prec } $$ on the set of affinizations, defined by Chari. In this Letter, we describe the minimal affinizations, with respect to $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \prec } $$ , when g is not simply-laced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750760
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