Does there exist an atomic Archimedean lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question is given.
We introduce dynamical analogues of the free orthogonal and free unitary quantum groups, which are no longer Hopf algebras but Hopf algebroids or quantum groupoids. These objects are constructed on the purely algebraic level and on the level of universal C*-algebras. As an example, we recover the dynamical studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases.
Summary of the three lectures. These notes are available electronically at http://www.ma.huji.ac.il/~drorbn/Talks/Srni-9901/notes.html.
It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
In these notes, conjectures about the exact semi-classical expansion of eigenvalues of hamiltonians corresponding to potentials with degenerate minima, are recalled. They were initially motivated by semi-classical calculations of quantum partition functions using a path integral representation and have later been proven to a large extent, using the theory of resurgent functions. They take the form of generalized Bohr--Sommerfeld quantization formulae. We explain here their...
We describe a new model of massless thermal bosons which predicts an hyperbolic fluctuation spectrum at low frequencies. It is found that the partition function per mode is the Euler generating function for unrestricted partitions ). Thermodynamical quantities carry a strong arithmetical structure : they are given by series with Fourier coefficients equal to summatory functions of the power of divisors, with for the free energy, for the number of particles and for the internal energy. Low...
Let be a -manifold with a Riemannian conformal structure . Given a regular curve on , the authors define a linear operator on the space of (differentiable) vector fields along , only depending on , called the Fermi-Walker connection along . Then, the authors introduce the concept of Fermi-Walker parallel vector field along , proving that such vector fields set up a linear space isomorphic to the tangent space at a point of . This allows to consider the Fermi-Walker horizontal lift of...