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  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear superposition formulas based on imprimitive group action (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3104-3122 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Systems of nonlinear ordinary differential equations are constructed for which the general solution is expressed algebraically in terms of a finite number of particular solutions. The equations and the corresponding nonlinear superposition formula are based on a nonlinear action of the Lie group SL(N,C) on a homogeneous space M. The isotropy group of the origin of this space is a nonmaximal parabolic subgroup of SL(N,C). Such equations can occur as Bäcklund transformations for soliton equations on flag manifolds. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532749
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  • 2
    Electronic Resource
    Electronic Resource
    Representations of the q-deformed algebra Uq′(so4) (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5389-5416 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the nonstandard q-deformation Uq′(so4) of the universal enveloping algebra U(so4) obtained by deforming the defining relations for skew-symmetric generators of U(so4). This algebra is used in quantum gravity and algebraic topology. We construct a homomorphism φ of Uq′(so4) to the certain nontrivial extension of the Drinfeld–Jimbo quantum algebra Uq(sl2)⊗2 and show that this homomorphism is an isomorphism. By using this homomorphism we construct irreducible finite-dimensional representations of the classical type and of the nonclassical type for the algebra Uq′(so4). It is proved that for q not a root of unity each irreducible finite-dimensional representation of Uq′(so4) is equivalent to one of these representations. We prove that every finite-dimensional representation of Uq′(so4) for q not a root of unity is completely reducible. It is shown how to construct (by using the homomorphism φ) tensor products of irreducible representations of Uq′(so4). [Note that no Hopf algebra structure is known for Uq′(so4).] These tensor products are decomposed into irreducible constituents. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1402631
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  • 3
    Electronic Resource
    Electronic Resource
    Representations of the cyclically symmetric q-deformed algebra soq(3) (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2135-2161 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An algebra homomorphism ψ from the nonstandard q-deformed (cyclically symmetric) algebra Uq(so3) to the extension Ûq(sl2) of the Hopf algebra Uq(sl2) is constructed. Not all irreducible representations of Uq(sl2) can be extended to representations of Ûq(sl2). Composing the homomorphism ψ with irreducible representations of Ûq(sl2) we obtain representations of Uq(so3). Not all of these representations of Uq(so3) are irreducible. Reducible representations of Uq(so3) are decomposed into irreducible components. In this way we obtain all irreducible representations of Uq(so3) when q is not a root of unity. A part of these representations turns into irreducible representations of the Lie algebra so3 when q→1. Representations of the other part have no classical analog. Using the homomorphism ψ it is shown how to construct tensor products of finite-dimensional representations of Uq(so3). Irreducible representations of Uq(so3) when q is a root of unity are constructed. Some of them are obtained from irreducible representations of Ûq(sl2) by means of the homomorphism ψ. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532856
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  • 4
    Electronic Resource
    Electronic Resource
    On the classification of irreducible finite-dimensional representations of Uq′(so3) algebra (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 472-500 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In an earlier work [M. Havlícek et al., J. Math. Phys. 40, 2135 (1999)] we defined for any finite dimension five nonequivalent irreducible representations of the nonstandard deformation Uq′(so3) of the Lie algebra so3 where q is not a root of unity [for each dimension only one of them (called classical) admits limit q→1]. In the first part of this paper we show that any finite-dimensional irreducible representation is equivalent to some of these representations. In the case qn=1 we derive new Casimir elements of Uq′(so3) and show that a dimension of any irreducible representation is not higher than n. These elements are Casimir elements of Uq′(som) for all m and even of Uq′(isom+1) due to Inönu–Wigner contraction. According to the spectrum of one of the generators, the representations are found to belong to two main disjoint sets. We give full classification and explicit formulas for all representations from the first set (we call them nonsingular representations). If n is odd, we have full classification also for the remaining singular case with the exception of a finite number of representations. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1328078
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  • 5
    Electronic Resource
    Electronic Resource
    An embedding of the Poincaré Lie algebra into an extension of the Lie field of SO0(1,4) (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 5320-5332 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The * isomorphism between algebraic extensions of the Lie fields of SO0(1,4) and the Poincaré group are considered herein. It is shown that the principal series of unitary ray representations of SO0(1,4) are associated, via the * isomorphism, with real mass, positive and negative energy representations of the Poincaré Lie algebra with arbitrary spin. Results on the most degenerate exceptional series of SO0(1,4) representations are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530307
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  • 6
    Electronic Resource
    Electronic Resource
    Irreducible *-representations of the Lie superalgebras B(0,n) with finite-degenerated vacuum. II (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 546-559 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The method presented in the first part of this work is applied to the superalgebra B(0,2). Two families of irreducible *-representations of this superalgebra and its real form osp(1,4) are constructed explicitly in terms of differential operators on the Hilbert space L2(M˜)⊗CN of N-component vector functions Ψ: M˜→CN@B: (i) the family {πJ@B: J=0,1,...} of massless representations with N=2, M˜=R+×(−π,π)×R+, the dimension of the vacuum subspace of πJ being J+1; (ii) the family {π(cursive-theta)0@B: cursive-theta〉0} of massive representations such that π(cursive-theta)0(up harp-r)so(3,2) equals the direct sum of three irreducible representations of so(3,2). This family is characterized by N=4, M˜=R+×(0,π)×R+ and nondegenerated vacuum. It is also shown that all the remaining massive representations form a system of families {π(cursive-theta)J@B: cursive-theta〉J/2}, J=1,2,..., with N=4(J+1), (J+1)-fold degenerated vacuum and common M˜=R+×(0,π)×R+.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528048
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  • 7
    Electronic Resource
    Electronic Resource
    Irreducible *-representations of Lie superalgebras B(0,n) with finite-degenerated vacuum (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2823-2831 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The problem of getting irreducible *-representations π of Lie superalgebras B(0,n), n=1,2, is studied, starting with a recently constructed family of linear representations in terms of differential operators on the space C∞N of CN -valued C∞ -functions. Equivalent formulation via creation-annihilation operators of a para-Bose system with n degrees of freedom is used, and the domain D of any π is shown to be a subset of C∞N containing a nonzero vacuum subspace. By assuming its dimension finite, the necessary conditions for existence of π are derived. The method is applied to the superalgebra B(0,1) and a one-parameter family Π of nonequivalent irreducible *-representations in terms of unbounded linear operators on L2(R+)⊗C2 is obtained. Each representation π∈Π has a nondegenerated vacuum and for all z∈B(0,1) satisfying z=z*, the operators π(z) are essentially self-adjoint.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527257
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  • 8
    Electronic Resource
    Electronic Resource
    Binding to mitochondrial proteins of lecithins containing known fatty acids
    Amsterdam : Elsevier
    Chemistry and Physics of Lipids 7 (1971), S. 144-158 
    Details
    ISSN: 0009-3084
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0009-3084(71)90028-4
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  • 9
    Electronic Resource
    Electronic Resource
    Eigenvalues of the Schrodinger operator via the Prufer transformation
    Amsterdam : Elsevier
    Physics Letters A 82 (1981), S. 64-66 
    Details
    ISSN: 0375-9601
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0375-9601(81)90938-5
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  • 10
    Electronic Resource
    Electronic Resource
    The tensor product of one-particle representations of an infinite-dimensional Lie algebra (1967)
    Springer
    Czechoslovak journal of physics 17 (1967), S. 809-821 
    Details
    ISSN: 1572-9486
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The recently proposed infinite-dimensional Lie algebra as a model of a symmetry scheme is studied from the point of view of its representations. We construct the tensor product of two one-particle representations of this algebra and study the reduction problem. A new series of representations having non-linear mass formulas is found. Some physical consequences for two-particle states are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01691631
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