Representations of hom-Lie algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-109

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

[[abstract]]Using conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yang et al.'s simplified geometric stiffness matrix [kg]12×12 of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14 of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14 matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14 matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]GB

Hom-quantum groups I: quasi-triangular Hom-bialgebras

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi-triangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel'd's quantum enveloping algebras. Each quasi-triangular Hom-bialgebra comes with a solution of the quantum Hom-Yang-Baxter equation, which is a non-associative version of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from modules of suitable quasi-triangular Hom-bialgebras.Comment: 21 page

Deformation of dual Leibniz algebra morphisms

An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.Comment: 10 pages. To appear in Communications in Algebr

Positivity of Quasilocal Mass

Motivated by the important work of Brown adn York on quasilocal energy, we propose definitions of quasilocal energy and momentum surface energy of a spacelike 2-surface with positive intrinsic curvature in a spacetime. We show that the quasilocal energy of the boundary of a compact spacelike hypersurface which satisfies the local energy condition is strictly positive unless the spacetime is flat along the spacelike hypersurface.Comment: 4 pages; final published versio

Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras

We present a procedure to construct (n+1)-Hom-Nambu-Lie algebras from n-Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n+k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions

Zooming in on local level statistics by supersymmetric extension of free probability

We consider unitary ensembles of Hermitian NxN matrices H with a confining potential NV where V is analytic and uniformly convex. From work by Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit of the characteristic function for a finite-rank Fourier variable K is determined by the Voiculescu R-transform, a key object in free probability theory. Going beyond these results, we argue that the same holds true when the finite-rank operator K has the form that is required by the Wegner-Efetov supersymmetry method of integration over commuting and anti-commuting variables. This insight leads to a potent new technique for the study of local statistics, e.g., level correlations. We illustrate the new technique by demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section

Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

In this paper we construct ternary $q$-Virasoro-Witt algebras which $q$-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using $su(1,1)$ enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary $q$-Virasoro-Witt algebras constructed in this article are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield Hom-Nambu Lie algebra structure for $q$-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary $q$-Virasoro-Witt algebras we construct, carry a structure of ternary Hom-Nambu-Lie algebra for all values of the involved parameters

Spintronic single qubit gate based on a quantum ring with spin-orbit interaction

In a quantum ring connected with two external leads the spin properties of an incoming electron are modified by the spin-orbit interaction resulting in a transformation of the qubit state carried by the spin. The ring acts as a one qubit spintronic quantum gate whose properties can be varied by tuning the Rashba parameter of the spin-orbit interaction, by changing the relative position of the junctions, as well as by the size of the ring. We show that a large class of unitary transformations can be attained with already one ring -- or a few rings in series -- including the important cases of the Z, X, and Hadamard gates. By choosing appropriate parameters the spin transformations can be made unitary, which corresponds to lossless gates.Comment: 4 pages, 4 figure

Enhanced hippocampal long-term potentiation and spatial learning in aged 11ß-hydroxysteroid dehydrogenase type 1 knock-out mice

Glucocorticoids are pivotal in the maintenance of memory and cognitive functions as well as other essential physiological processes including energy metabolism, stress responses, and cell proliferation. Normal aging in both rodents and humans is often characterized by elevated glucocorticoid levels that correlate with hippocampus-dependent memory impairments. 11ß-Hydroxysteroid dehydrogenase type 1 (11ß-HSD1) amplifies local intracellular ("intracrine") glucocorticoid action; in the brain it is highly expressed in the hippocampus. We investigated whether the impact of 11ß-HSD1 deficiency in knock-out mice (congenic on C57BL/6J strain) on cognitive function with aging reflects direct CNS or indirect effects of altered peripheral insulin-glucose metabolism. Spatial learning and memory was enhanced in 12 month "middle-aged" and 24 month "aged" 11ß-HSD1<sup>–/–</sup> mice compared with age-matched congenic controls. These effects were not caused by alterations in other cognitive (working memory in a spontaneous alternation task) or affective domains (anxiety-related behaviors), to changes in plasma corticosterone or glucose levels, or to altered age-related pathologies in 11ß-HSD1<sup>–/–</sup> mice. Young 11ß-HSD1<sup>–/–</sup> mice showed significantly increased newborn cell proliferation in the dentate gyrus, but this was not maintained into aging. Long-term potentiation was significantly enhanced in subfield CA1 of hippocampal slices from aged 11ß-HSD1<sup>–/–</sup> mice. These data suggest that 11ß-HSD1 deficiency enhances synaptic potentiation in the aged hippocampus and this may underlie the better maintenance of learning and memory with aging, which occurs in the absence of increased neurogenesis