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  • Articles  (9)
  • 16W30  (9)
  • Springer  (9)
  • American Geophysical Union (AGU)
  • Annual Reviews
  • 1995-1999  (9)
  • 1980-1984
  • 1935-1939
  • 1995  (9)
  • Mathematics  (9)
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  • Articles  (9)
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  • Springer  (9)
  • American Geophysical Union (AGU)
  • Annual Reviews
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  • 1995-1999  (9)
  • 1980-1984
  • 1935-1939
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Topic
  • 1
    Electronic Resource
    Electronic Resource
    Lie groups whose coadjoint orbits are of dimension smaller or equal to two (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 183-186 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 17Bxx ; 17B05 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give a complete classification of the class of connected, simply connected Lie groups whose coadjoint orbits are of dimension smaller or equal to two.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739806
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  • 2
    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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  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    A star-product approach to noncompact quantum groups (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 231-240 
    Details
    ISSN: 1573-0530
    Keywords: AMS classification 17B37 ; 16W30 ; 22D05 ; 46H99 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Using the duality and the topological theory of well-behaved Hopf algebras, we construct star-product models of noncompact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple Lie algebras. Our star-products act not only on coefficient functions of finite-dimensional representations, but actually on allC ∞ functions, and they even exist for nonlinear (semi-simple) Lie groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749624
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  • 5
    Electronic Resource
    Electronic Resource
    Bicovariant differential geometry of the quantum group SL h (2) (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 303-311 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 58B30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract There are only two quantum group structures on the space of two by two unimodular matrices, these are the SL q (2) and the SL h (2) quantum groups. The differential geometry of SL q (2) is well known. In this Letter, we develop the differential geometry of SL h (2), and show that the space of left invariant vector fields is three-dimensional.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750837
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  • 6
    Electronic Resource
    Electronic Resource
    Comparison of dynamical entropies for the noncommutative shifts (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 241-247 
    Details
    ISSN: 1573-0530
    Keywords: 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that two definitions of dynamical entropy for noncommutative shifts give different results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749625
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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
    Colour lie algebras andR-matrices (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 249-254 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 16S30 ; 17B70 ; 17B35 ; 82B23
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The universal enveloping algebra of a colour Lie algebra is extended by a ‘bosonization’ process to a nongraded quasitriangular Hopf algebra, and the explicit form of theR-matrix for the Hopf algebra is found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749626
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  • 9
    Electronic Resource
    Electronic Resource
    Multiparameter quantum groups and multiparameterR-matrices (1995)
    Springer
    Acta applicandae mathematicae 41 (1995), S. 57-98 
    Details
    ISSN: 1572-9036
    Keywords: 16W30 ; 58F07 ; 57M25 ; multiparameter quantum group ; multiparameterR-matrix ; Yang-Baxter equation ; Hopf algebra ; bialgebra ; PBW-algebra ; knot invariant ; link invariant ; confluent rewriting system ; fundamental communication relations (FCR) ; diamond lemma ; generalized quantum space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract There exists an ( 2 n ) + 1 parameter quantum group deformation of GLn which has been constructed independently by several (groups of) authors. In this note, I give an explicitR-matrix for this multiparameter family. This gives additional information on the nature of this family and facilitates some calculations. This explicitR-matrix satisfies the Yang-Baxter equation. The centre of the paper is Section 3 which describes all solutions of the YBE under the restriction r cd ab =0 unlessa, b=c, d. One kind of the most general constituents of these solutions precisely corresponds to the ( 2 n ) + 1 parameter quantum group mentioned above. I describe solutions which extend to an enhanced Yang-Baxter operator and, hence, define link invariants. The paper concludes with some preliminary results on these link invariants.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00996106
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