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  • 1
    Electronic Resource
    Electronic Resource
    The complete root systems of the affine Kac–Moody superalgebras (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1817-1838 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: By using certain special automorphisms, the complete root structures of all the affine Kac–Moody superalgebras, both twisted and untwisted, are derived in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528679
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  • 2
    Electronic Resource
    Electronic Resource
    Sugawara-type constructions of the Virasoro algebra based on the twisted affine Kac–Moody superalgebras (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1121-1149 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Explicit realizations of representations of the Virasoro algebra are obtained using highest-weight representations of the twisted affine Kac–Moody superalgebras A(2)(2l−1/0) (for l≥2), A(4)(2l/0) (for l≥1), and C(2)(l+1) (for l≥1) in a generalization of the Sugawara construction. It is also shown that A(2)(2l−1/0) (for l≥2) and A(4)(2l/0) (for l≥1) can be modified to produce "Neveu–Schwarz'' type superalgebras, and the corresponding Sugawara construction is given for these. For C(2)(l+1) (for l≥1) it is demonstrated that no such "Neveu–Schwarz'' modification is possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529309
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  • 3
    Electronic Resource
    Electronic Resource
    On chains of orthosymplectic Lie superalgebras and the n-dimensional quantum harmonic oscillator (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1655-1661 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Triplets of embedded orthosymplectic Lie superalgebras are singled out and analyzed in terms of their respective even and odd root systems. The corresponding chains of embeddings are considered for arbitrary integers m and n (for both m≠n and m=n). It is shown that the second member inside each triplet is always in a one-to-one correspondence with the semidirect sum of the third member and the associated Heisenberg superalgebra that is characterized by the same entries m and n. For arbitrary m=n, invariance superalgebras of the n-dimensional harmonic oscillator are recovered and their one-to-one correspondence associated with a recent "character reversal'' phenomenon linking these invariance superstructures is rigorously explained. Specific and general cases as well as conclusions are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528250
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  • 4
    Electronic Resource
    Electronic Resource
    Twisting 2-cocycles for the construction of new non-standard quantum groups (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5383-5401 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We introduce a new class of 2-cocycles defined explicitly on the generators of certain multiparameter standard quantum groups. These allow us, through the process of twisting the familiar standard quantum groups, to generate new as well as previously known examples of non-standard quantum groups. In particular we are able to construct generalisations of both the Cremmer-Gervais deformation of SL(3) and the so called esoteric quantum groups of Fronsdal and Galindo in an explicit and straightforward manner. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531949
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  • 5
    Electronic Resource
    Electronic Resource
    Abstract carrier space formalism for the irreducible tensor operators of compact quantum group algebras (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 2934-2954 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that there are two types of irreducible tensor operator, which may be called ‘ordinary' and ‘twisted'. The consistency of the definitions is demonstrated, and various consequences are deduced, including generalizations of the Wigner–Eckart theorem for both the ordinary and twisted operators. Examples of irreducible tensor operators for the standard deformation of the function algebra of the compact Lie group SU(2) are described to demonstrate the applicability of the new definitions. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531547
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  • 6
    Electronic Resource
    Electronic Resource
    Irreducible tensor operators in the regular coaction formalisms of compact quantum group algebras (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 4590-4634 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms. In each case it is shown that there are two types of irreducible tensor operator, which may be called "ordinary'' and "twisted.'' The consistency of the definitions is demonstrated, and various consequences are deduced, including generalizations of the Wigner–Eckart theorem for both the ordinary and twisted operators. Also included are discussions (within the regular coaction formalisms for compact quantum group algebras) of inner-products, basis functions, projection operators, Clebsch–Gordan coefficients, and two types of tensor product of corepresentations. The formulation of quantum homogeneous spaces for compact quantum group algebras is discussed, and the defining conditions for the irreducible tensor operators associated with such quantum homogeneous spaces and with the unitary irreducible corepresentations of the compact quantum group algebras are then deduced. There are two versions, which correspond to restrictions of the right and left regular coactions. In each case it is again shown that there are ordinary and twisted irreducible tensor operators. Various consequences are deduced, including the corresponding generalizations of the Wigner–Eckart theorem. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531643
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  • 7
    Electronic Resource
    Electronic Resource
    Multiparameter deformations of the universal enveloping algebras of the simple Lie algebras Al for all l≥2 and the Yang–Baxter equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3963-3977 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A {1+1/2l(l−1)}-parameter deformation of the universal enveloping algebra of the simple Lie algebra Al(=sl(l+1,C)) is derived for all l≥2, starting from a certain multiparameter matrix that satisfies the quantum Yang–Baxter equation. It is shown that this Hopf algebra has the same product relations and antipode as the standard one-parameter deformation Uq(sl(l+1,C)), but has a different coproduct. It is also shown that for all l≥2 there exists a 1/2l(l−1)-parameter Hopf algebra whose product relations are merely the commutation relations of Al itself, but whose coproduct is different from the usual one for the universal enveloping algebra of Al.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529845
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  • 8
    Electronic Resource
    Electronic Resource
    An Energy Band Interpolation Scheme, with Application to Body-centred Cubic Lithium (1960)
    [s.l.] : Nature Publishing Group
    Nature 186 (1960), S. 379-380 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] The method has been applied to body-centred cubic lithium, for which energy-levels at high-symmetry points have been obtained by Glasser and Callaway5,6, using the orthogonalized plane wave method and the corrected Seitz potential7, and with a stated accuracy ± 0-05 Ry. The number of terms ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/186379a0
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  • 9
    Electronic Resource
    Electronic Resource
    The symmetry of the Fermi surface of a system of interacting electrons in a crystal (1964)
    Springer
    The European physical journal 2 (1964), S. 161-165 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Description / Table of Contents: Résumé Il est démontré que la surface de Fermi définie parLuttinger pour un système d’électrons dans un cristal, compte tenu de leur interaction, est invariante à toute opération du groupe ponctuel du cristal.
    Abstract: Zusammenfassung Es wird gezeigt, daß die vonLuttinger definierte Fermifläche für ein System von Elektronen eines Kristalls, deren Wechselwirkung vollständig berücksichtigt wird, gegenüber allen Operationen der Punktgruppe des Kristalls invariant ist.
    Notes: Abstract It is shown that the Fermi surface defined byLuttinger for a system of interacting electrons in a crystal is invariant under all the operations of the point group of the crystal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02422873
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  • 10
    Electronic Resource
    Electronic Resource
    A two-parameter deformation of the universal enveloping algebra ofsl(3, C) (1992)
    Springer
    The European physical journal 56 (1992), S. 245-252 
    Details
    ISSN: 1434-6052
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Starting from a certain multi-parameter matrix that satisfies the quantum Yang-Baxter equation, a two-parameter deformation of the universal enveloping algebra of the simple Lie algebrasl(3, C) is derived. It is shown that this has same product relations and antipode as the standard one-parameter deformationU q(sl(3, C)) but has a different coproduct. It is also shown that there exists a Hopf algebra whose product relations are merely the commutation relations ofsl(3, C) itself, but whose coproduct is different from the usual one for the universal enveloping algebra ofsl(3, C).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01555521
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