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We study the discrete groups whose duals embed into a given compact quantum group, . In the matrix case the embedding condition is equivalent to having a quotient map , where is a certain family of groups associated to . We develop here a number of techniques for computing , partly inspired from Bichon’s classification of group dual subgroups . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot have non-abelian...
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.
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...
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.
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...
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...
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...
The conformal infinity of a quaternionic-Kähler metric on a -manifold with boundary is a codimension distribution on the boundary called quaternionic contact. In dimensions greater than , a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension , 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...
Let and be hyperkähler manifolds. We study stationary quaternionic maps between and . 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 . 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...
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