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Quantum isometries and group dual subgroups

Teodor Banica, Jyotishman Bhowmick, Kenny De Commer (2012)

Annales mathématiques Blaise Pascal

We study the discrete groups $Λ$ whose duals embed into a given compact quantum group, $\hat{Λ} \subset G$ . In the matrix case $G \subset U_{n}^{+}$ the embedding condition is equivalent to having a quotient map $Γ_{U} \to Λ$ , where $F = {Γ_{U} ∣ U \in U_{n}}$ is a certain family of groups associated to $G$ . We develop here a number of techniques for computing $F$ , partly inspired from Bichon’s classification of group dual subgroups $\hat{Λ} \subset S_{n}^{+}$ . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot have non-abelian...

Quantum isometry group for spectral triples with real structure.

Goswami, Debashish (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Quantum mechanics in strong time dependent external fields

Yves Pomeau (1986)

Annales de l'I.H.P. Physique théorique

Quantum Mechanics of Guiding Center Motion in Strong Magnetic Field (Coherent State Path Integral Approach)

Kuratsuji, Hiroshi, Tochishita, Teruyuki, Mizui, Masayuki (1997)

Serdica Mathematical Journal

A new approach is proposed for the quantum mechanics of guiding center motion in strong magnetic field. This is achieved by use of the coherent state path integral for the coupled systems of the cyclotron and the guiding center motion. We are specifically concerned with the effective action for the guiding center degree, which can be used to get the Bohr- Sommerfeld quantization scheme. The quantization rule is similar to the one for the vortex motion as a dynamics of point particles.

Quantum spacetime: a disambiguation.

Piacitelli, Gherardo (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Quantum stochastic dynamics. I.

Majewski, Adam W., Zegarlinski, Boguslaw (1995)

Mathematical Physics Electronic Journal [electronic only]

Quantum ultrametrics on AF algebras and the Gromov-Hausdorff propinquity

Konrad Aguilar, Frédéric Latrémolière (2015)

Studia Mathematica

We construct quantum metric structures on unital AF algebras with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite-dimensional C*-algebras for the quantum propinquity. We then study the geometry, for the quantum propinquity, of three natural classes of AF algebras equipped with our quantum metrics: the UHF algebras, the Effrös-Shen AF algebras associated with continued fraction expansions of irrationals, and the Cantor...

Quantum vacuum polarization at the Black-Hole horizon

Alain Bachelot (1997)

Annales de l'I.H.P. Physique théorique

Quantum Weyl group and some [of] its applications

Soibelman, Ya. S. (1991)

Proceedings of the Winter School "Geometry and Physics"

Quasi singularities

Vladimir M. Zakalyukin (2008)

Banach Center Publications

A classification of simple equivalence classes of function germs with respect to new relations is given. The equivalence relation is similar but weaker than the right action of diffeomorphisms which preserve the boundary. It is used in classifying Lagrange projections with boundary. The simple classes of function germs with respect to the equivalence similar to fibration preserving action are also discussed.

Quasi-algebraic representability of sets in $R^{n}$ .

W. Waliszewski (1984)

Banach Center Publications

Quasi-bigèbres jacobiennes

Yvette Kosmann-Schwarzbach (1992)

Recherche Coopérative sur Programme n°25

Quasilinear Resolutions of Non-Linear Equations.

Robert J. Elliott (1974)

Manuscripta mathematica

Quasilinear waves and trapping: Kerr-de Sitter space

Peter Hintz, András Vasy (2014)

Journées Équations aux dérivées partielles

In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally...

Quasistatic frictional problems for elastic and viscoelastic materials

Oanh Chau, Dumitru Motreanu, Mircea Sofonea (2002)

Applications of Mathematics

We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational...

Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics

Matteo Negri (2014)

ESAIM: Control, Optimisation and Calculus of Variations

We characterize quasi-static rate-independent evolutions, by means of their graph parametrization, in terms of a couple of equations: the first gives stationarity while the second provides the energy balance. An abstract existence result is given for functionals ℱ of class C1 in reflexive separable Banach spaces. We provide a couple of constructive proofs of existence which share common features with the theory of minimizing movements for gradient flows. Moreover, considering a sequence of functionals...

Quaternionic contact structures in dimension $7$

David Duchemin (2006)

Annales de l’institut Fourier

The conformal infinity of a quaternionic-Kähler metric on a $4 n$ -manifold with boundary is a codimension $3$ distribution on the boundary called quaternionic contact. In dimensions $4 n - 1$ greater than $7$ , a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension $7$ , we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic-Kähler metric. This allows us to find the quaternionic-contact structures...

Quaternionic geometry of a nilpotent variety.

Andrew Swann, Piotr Z. Kobak (1993)

Mathematische Annalen

Quaternionic maps and minimal surfaces

Jingyi Chen, Jiayu Li (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $(M, J^{α}, α = 1, 2, 3)$ and $(N, 𝒥^{α}, α = 1, 2, 3)$ be hyperkähler manifolds. We study stationary quaternionic maps between $M$ and $N$ . We first show that if there are no holomorphic 2-spheres in the target then any sequence of stationary quaternionic maps with bounded energy subconverges to a stationary quaternionic map strongly in $W^{1, 2} (M, N)$ . We then find that certain tangent maps of quaternionic maps give rise to an interesting minimal 2-sphere. At last we construct a stationary quaternionic map with a codimension-3 singular set by using the embedded...

Quelques aspects de la théorie des points fixes dans les espaces de Banach - II

J. B. Baillon (1978/1979)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

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