283 research outputs found

    Thermodynamic Properties of a Quantum Group Boson Gas GLp,q(2)GL_{p,q}(2)

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    An approach is proposed enabling to effectively describe the behaviour of a bosonic system. The approach uses the quantum group GLp,q(2)GL_{p,q}(2) formalism. In effect, considering a bosonic Hamiltonian in terms of the GLp,q(2)GL_{p,q}(2) generators, it is shown that its thermodynamic properties are connected to deformation parameters pp and qq. For instance, the average number of particles and the pressure have been computed. If pp is fixed to be the same value for qq, our approach coincides perfectly with some results developed recently in this subject. The ordinary results, of the present system, can be found when we take the limit p=q=1p=q=1.Comment: 13 pages, Late

    Differential Calculus on the Quantum Superspace and Deformation of Phase Space

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    We investigate non-commutative differential calculus on the supersymmetric version of quantum space where the non-commuting super-coordinates consist of bosonic as well as fermionic (Grassmann) coordinates. Multi-parametric quantum deformation of the general linear supergroup, GLq(m∣n)GL_q(m|n), is studied and the explicit form for the R^{\hat R}-matrix, which is the solution of the Yang-Baxter equation, is presented. We derive the quantum-matrix commutation relation of GLq(m∣n)GL_q(m|n) and the quantum superdeterminant. We apply these results for the GLq(m∣n)GL_q(m|n) to the deformed phase-space of supercoordinates and their momenta, from which we construct the R^{\hat R}-matrix of q-deformed orthosymplectic group OSpq(2n∣2m)OSp_q(2n|2m) and calculate its R^{\hat R}-matrix. Some detailed argument for quantum super-Clifford algebras and the explict expression of the R^{\hat R}-matrix will be presented for the case of OSpq(2∣2)OSp_q(2|2).Comment: 17 pages, KUCP-4

    Quantum Deformed su(m∣n)su(m|n) Algebra and Superconformal Algebra on Quantum Superspace

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    We study a deformed su(m∣n)su(m|n) algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. {}From the deformed su(1∣4)su(1|4) algebra, we derive deformed Lorentz, translation of Minkowski space, iso(2,2)iso(2,2) and its supersymmetric algebras as closed subalgebras with consistent automorphisms.Comment: 27 pages, KUCP-59, LaTeX fil

    The exponential map for representations of Up,q(gl(2))U_{p,q}(gl(2))

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    For the quantum group GLp,q(2)GL_{p,q}(2) and the corresponding quantum algebra Up,q(gl(2))U_{p,q}(gl(2)) Fronsdal and Galindo explicitly constructed the so-called universal TT-matrix. In a previous paper we showed how this universal TT-matrix can be used to exponentiate representations from the quantum algebra to get representations (left comodules) for the quantum group. Here, further properties of the universal TT-matrix are illustrated. In particular, it is shown how to obtain comodules of the quantum algebra by exponentiating modules of the quantum group. Also the relation with the universal RR-matrix is discussed.Comment: LaTeX-file, 7 pages. Submitted for the Proceedings of the 4th International Colloquium ``Quantum Groups and Integrable Systems,'' Prague, 22-24 June 199

    On the Differential Geometry of GLq(1∣1)GL_q(1| 1)

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    The differential calculus on the quantum supergroup GLq(1∣1)_q(1| 1) was introduced by Schmidke {\it et al}. (1990 {\it Z. Phys. C} {\bf 48} 249). We construct a differential calculus on the quantum supergroup GLq(1∣1)_q(1| 1) in a different way and we obtain its quantum superalgebra. The main structures are derived without an R-matrix. It is seen that the found results can be written with help of a matrix R^\hat{R}Comment: 14 page

    Lagrangian and Hamiltonian Formalism on a Quantum Plane

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    We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane Qq,pQ_{q,p}. For Lagrangian mechanics, we first define a tangent quantum plane TQq,pTQ_{q,p} spanned by noncommuting particle coordinates and velocities. Using techniques similar to those of Wess and Zumino, we construct two different differential calculi on TQq,pTQ_{q,p}. These two differential calculi can in principle give rise to two different particle dynamics, starting from a single Lagrangian. For Hamiltonian mechanics, we define a phase space T∗Qq,pT^*Q_{q,p} spanned by noncommuting particle coordinates and momenta. The commutation relations for the momenta can be determined only after knowing their functional dependence on coordinates and velocities. Thus these commutation relations, as well as the differential calculus on T∗Qq,pT^*Q_{q,p}, depend on the initial choice of Lagrangian. We obtain the deformed Hamilton's equations of motion and the deformed Poisson brackets, and their definitions also depend on our initial choice of Lagrangian. We illustrate these ideas for two sample Lagrangians. The first system we examine corresponds to that of a nonrelativistic particle in a scalar potential. The other Lagrangian we consider is first order in time derivative

    Estrogens regulate early embryonic development of the olfactory sensory system via estrogen-responsive glia.

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    This is the final version. Available from The Company of Biologists via the DOI in this record. Estrogens are well-known to regulate development of sexual dimorphism of the brain; however, their role in embryonic brain development prior to sex-differentiation is unclear. Using estrogen biosensor zebrafish models, we found that estrogen activity in the embryonic brain occurs from early neurogenesis specifically in a type of glia in the olfactory bulb (OB), which we name estrogen-responsive olfactory bulb (EROB) cells. In response to estrogen, EROB cells overlay the outermost layer of the OB and interact tightly with olfactory sensory neurons at the olfactory glomeruli. Inhibiting estrogen activity using an estrogen receptor antagonist, ICI182,780 (ICI), and/or EROB cell ablation impedes olfactory glomerular development, including the topological organisation of olfactory glomeruli and inhibitory synaptogenesis in the OB. Furthermore, activation of estrogen signalling inhibits both intrinsic and olfaction-dependent neuronal activity in the OB, whereas ICI or EROB cell ablation results in the opposite effect on neuronal excitability. Altering the estrogen signalling disrupts olfaction-mediated behaviour in later larval stage. We propose that estrogens act on glia to regulate development of OB circuits, thereby modulating the local excitability in the OB and olfaction-mediated behaviour.Biotechnology and Biological Sciences Research CouncilBiotechnology and Biological Sciences Research CouncilUniversity of Exete

    Automorphisms of associative algebras and noncommutative geometry

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    A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the hh-deformed plane and the quantum group GLpq(2) are recovered in this way. Geometric structures like metrics and compatible linear connections are introduced.Comment: 28 pages, some references added, several amendments of minor importance, remark on modular group in section 8 omitted, to appear in J. Phys.
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