Search results for "F06"
showing 10 items of 10 documents
Quantization of Poisson Lie Groups and Applications
1996
LetG be a connected Poisson-Lie group. We discuss aspects of the question of Drinfel'd:can G be quantized? and give some answers. WhenG is semisimple (a case where the answer isyes), we introduce quantizable Poisson subalgebras ofC ∞(G), related to harmonic analysis onG; they are a generalization of F.R.T. models of quantum groups, and provide new examples of quantized Poisson algebras.
On the arithmetic and geometry of binary Hamiltonian forms
2011
Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.
Internacionalización de empresas a través de clústeres: análisis bibliométrico de palabras clave de 152 publicaciones destacadas en el período 2009-2…
2022
[EN] While countless studies on the role of clusters in regional economic developments and business performance have been done, some disadvantages and limitations also have been identified. Limitations such as small local markets, limited resources, isolation, and over-independence which lead companies to a lock-in state regarding knowledge and innovation can be solved by means of internationalization or foreign market expansion. Therefore, the internationalization of clusters still needs more attention. Furthermore, by conducting a bibliometric study based on the keywords from previous research, this investigation intends to identify the principal and most influential items, their relation…
Irrigation water saving strategies in Citrus orchards: Analysis of the combined effects of timing and severity of soil water deficit
2021
[EN] The knowledge of the crop response to soil water deficit is essential to predict the actual crop water requirements under limited soil water conditions. The mathematical schematization of the crop response under RDI can allow identifying the exact irrigation timing. The threshold of soil water status below which crop transpiration decreases represents a key parameter for the water stress functions. The main objective of this paper was to investigate the effects of several RDI treatments, applied during the three stages of fruit growth, on soil-plant-water relations of drip-irrigated mandarin trees. Experiments were carried out in seven irrigation treatments: a control, irrigated at 125…
Counting and equidistribution in Heisenberg groups
2014
We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension $2$. We prove a Mertens' formula for the integer points over a quadratic imaginary number fields $K$ in the light cone of Hermitian forms, as well as an equidistribution theorem of the set of rational points over $K$ in Heisenberg groups. We give a counting formula for the cubic points over $K$ in the complex projective plane whose Galois conjugates are orthogonal and isotropic for a given Hermitian form over $K$, and a counting and equidistribution result for …
Counting and equidistribution in quaternionic Heisenberg groups
2020
AbstractWe develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.
Rigidité, comptage et équidistribution de chaînes de Cartan quaternioniques
2020
We prove an analog of Cartan's theorem, saying that the chain-preserving transformations of the boundary of the quaternionic hyperbolic spaces are projective transformations. We give a counting and equidistribution result for the orbits of arithmetic chains in the quaternionic Heisenberg group.; Nous montrons un analogue d'un théorème de Cartan, disant que les transformations préservant les chaînes sur le bord d'un espace hyperbolique quaternionien est une transformation projective. Nous donnons un résultat de comptage et d'équidistribution pour une orbite de chaînes arithmétiques dans le groupe de Heisenberg quaternionique.
Algebraic Quantization, Good Operators and Fractional Quantum Numbers
1995
The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the ``failure" of the Ehrenfest theorem is clarified in terms of the already defined notion of {\it good} (and {\it bad}) operators. The analysis of ``constrained" Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring ``anomal…
Quantization on the Virasoro group
1990
The quantization of the Virasoro group is carried out by means of a previously established group approach to quantization. We explicitly work out the two-cocycles on the Virasoro group as a preliminary step. In our scheme the carrier space for all the Virasoro representations is made out of polarized functions on the group manifold. It is proved that this space does not contain null vector states, even forc≦1, although it is not irreducible. The full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace ℋ(c, h), the orbit of the enveloping algebra through the vacuum, which is irreducible for any value ofc andh. ℋ(c, h) is a proper subspace of the sp…
Algebraic quantization on a group and nonabelian constraints
1989
A generalization of a previous group manifold quantization formalism is proposed. In the new version the differential structure is circumvented, so that discrete transformations in the group are allowed, and a nonabelian group replaces the ordinary (central)U(1) subgroup of the Heisenberg-Weyl-like quantum group. As an example of the former we obtain the wave functions associated with the system of two identical particles, and the latter modification is used to account for the Virasoro constraints in string theory.