We present three results stating when a concrete (=set-representable) quantum logic with covering properties (generalization of compatibility) has to be a Boolean algebra. These results complete and generalize some previous results [3, 5] and answer partiallz a question posed in [2].
Let and be mutually commuting unital C* subalgebras of (). It is shown that and are C* independent if and only if for all natural numbers n, m, for all n-tuples A = (A₁, ..., Aₙ) of doubly commuting nonzero operators of and m-tuples B = (B₁, ..., Bₘ) of doubly commuting nonzero operators of , , where Sp denotes the joint Taylor spectrum.
List of ParticipantsOrganizing committee: Vasil Tsanov – Sofia University (Chairman), Harry Aleksiev – High School for Management and Laguages in Zlatograd (Local Organizer), Leon Farhy – Sofia University (Scientific Secretary), Emil Horozov – Sofia University, Ivailo Mladenov – Bulgarian Academy of Sciences, Angel Zhivkov – Sofia University.
We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behaviour of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples in the case where the boundary is smooth as well as for polytopes; These...
We give a characterization of conformal blocks in terms of the singular cohomology of suitable smooth projective varieties, in genus for classical Lie algebras and .
Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials.
We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-riemannian manifold . In other words, we establish a canonical isomorphism between the spaces of polynomials on and of differential operators on tensor densities over , both viewed as modules over the Lie algebra where . This quantization exists for generic values of the weights of the tensor densities and we compute the critical values of the weights yielding...
Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.
A non-holonomic 3-web is defined by two operators and such that is a projector, is involutory, and they are connected via the relation . The so-called parallelizing connection with respect to which the 3-web distributions are parallel is defined. Some simple properties of such connections are found.