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  • 1
    Electronic Resource
    Electronic Resource
    Infinite-dimensional algebras and a trigonometric basis for the classical Lie algebras (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1088-1094 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper explores features of the infinite-dimensional algebras that have been previously introduced. In particular, it is shown that the classical simple Lie algebras (AN, BN, CN, DN) may be expressed in an "egalitarian'' basis with trigonometric structure constants. The transformation to the standard Cartan–Weyl basis, and the particularly transparent N→∞ limit that this formulation allows is provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528788
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Quantum algebra deforming maps, Clebsch–Gordan coefficients, coproducts, R and U matrices (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 676-688 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Quantum algebra deforming maps explicitly define comultiplications that differ from the usual noncocommutative coproducts. Map-induced coproducts are connected to the usual ones by similarity transformations U that may be expressed either in terms of Clebsch–Gordan coefficients, or in a universal operator form. The product of two such U matrices yields the R matrix for a fixed value of the spectral parameter, which bears on the Yang–Baxterization of U as well as R. All this is explicitly illustrated for the tensor product 1/2⊗j of SU(2)q using several deforming maps whose coproducts are continuously connected by similarity transformations to form a two-parameter manifold. Some observations are made on the general structure of U and R matrices, and of coproduct manifolds, based on the solutions of hierarchies of partial difference equations. Applications of deforming maps and U matrices to the physics of spin-chains are outlined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529410
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A presentation for the Virasoro and super-Virasoro algebras (1988)
    Springer
    Communications in mathematical physics 117 (1988), S. 595-614 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the entire Virasoro, Ramond and Neveu-Schwarz algebras can each be constructed from a finite number of well-chosen generators satisfying a small number of conditions. The most economical sets consist of just two starting generators in all cases, subject to eight conditions for the Virasoro case, five conditions for the Ramond case, and nine conditions for the Neveu-Schwarz case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01218387
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    Paper (German National Licenses)
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