THE MINIMAL CLOSED NON-TRIVIAL IDEALS OF TOEPLITZ ALGEBRAS ON DISCRETE GROUPS

Let G be a discrete group and (G, G+) an ordered group. Let (G, GF) be the minimal quasiordered group containing (G, G+). Let G+ (G) and (G) be the corresponding Toeplitz algebras, and γGF,G+ the natural C*-algebra morphism from G+ (G) to GF(G). This paper studies the connection between Ker GF,G+ and the minimal closed ideal ofTG+ (G). It is proved that if G is amenable and GF≠G+, then Ker γGF,G+ is exactly the minimal closed non-trivial ideal of G+ (G). As an application, in the last part of this paper, a character of K-groups of Toeplitz algebras on ordered groups is clarified.

PROOF OF A CONJECTURE RELATED TO THE PARABOLIC CLASS NUMBERS OF SOME FUCHSIAN GROUPS

This paper proves a conjecture given in [6], which is concerning with the parabolic class numbers of some Fuchsian groups.

Testing the Results of Measurements of Neutrino Parameters Using the Dirac CPV Phase Formula

Essentially the main intention of this paper was to test the formula for the Dirac CPV phase and see if it can reflect the results of experimental measurements of neutrino parameters. By knowing the mathematical formula for the Dirac CPV phase, a connection was established with some of the residual symmetry groups, which made it possible to develop a procedure for directly determining the range in which the numerical value for the Dirac CPV phase could be found. In this sense, two different sources of information containing measured data for neutrinos were used for the corresponding calculations, and then a comparative overview of the calculated results was presented. It is particularly emphasized that the formula for the Dirac CPV phase does not depend on the mixing angles that are incorporated into the PMNS matrix, but only on the ratio between the corresponding squares of the neutrino mass difference. All the numerous results obtained from the corresponding calculations for the Dirac CPV phase point to the justified introduction of the theory that is related to three neutrinos, and thus the agreement of our results with the STEREO experiment is justified, so that the hypothesis of the possible existence of a sterile neutrino in nature should be excluded.

Wiener-Hopf Operators on Discrete Abelian Groups

The groupoid approach to study Wiener-Hopf operators on discrete abelian groups is realized.

On Limit Sets and Discreteness Criteria for Nonelementary Subgroups of M(~n)

In this paper, we will study the nonelementary groups of MSbius transformations in R^n and some properties are obtained. Also in this paper we will prove several theorems about discreteness criteria and group convergence of nonelementary groups of M（R^n）.

The Rigidity of the Kernels of the Natural Morphisms between Toeplitz Algebras

Let (G, E) be a quasi-ordered group such that E∩E -1 is infinite, (G, G +) an ordered group with G +EG, and (G, G 1) the partially ordered group induced by (G, E).Let γ E, G + ∶T G + →T E and γ E, G 1 ∶T G 1 →T E be the corresponding natural morphisms between Toeplitz algebras. We prove that the kernel Ker γ E, G + is rigid,while Ker γ E, G 1 is equal to the compact-operator ideal on 2(G 1), and all Fredholm operators in the Toeplitz algebra T G 1 are of index zero.

Algebraic Properties of Toeplitz Operators on Discrete Commutative Groups

In this paper,a generalized Toeplitz operator is defined and some of results about the classical Toeplitz operator are generalized.In particular,we obtain the necessary and sufficient condition for the product of two such Toeplitz operators to still be Toeplitz operator and the necessary and sufficient condition for such Toeplitz operator to be normal operator.Finally,a necessary condition for two such Toeplitz operators to be commutative is established.

Quasi-morphisms via Local Action Data and Quasi-isometries

In this work we first present a principle which says that quasi-morphisms can be obtained via local data of group action on certain appropriate spaces. In a rough manner the principle says that instead of starting with a given group and trying to build or study its space of quasi-morphisms, we should start with a space with a certain structure, in such a way that groups acting on this space and respecting this structure will automatically carry quasi-morphisms, where these are supposed to be better understood. This principle plays an important role in the second result of this paper, which is a universal embedding of the projective space of the linear space of quasi-morphisms of any given countable group, into the space of quasi-isometries of a certain universal metric space.

Twisted bounded-dilation group C*-algebras as C*-metric algebras

We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra C*r(Γ, σ) for the pointwise multiplication operator Mlon l2(Γ), induced by a proper length function l on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.

Phenomenological aspects of possible vacua of a neutrino flavor model

We discuss a supersymmetric model with discrete flavor symmetry A4×Z3. The additional scalar fields which contribute masses of leptons in the Yukawa terms are introduced in this model. We analyze their scalar potential and find that they have various vacuum structures. We show the relations among 24 different vacua and classify them into two types. We derive expressions of the lepton mixing angles, Dirac CP violating phase and Majorana phases for the two types. The model parameters which are allowed by the experimental data of the lepton mixing angles are different for each type. We also study the constraints on the model parameters which are related to Majorana phases. The different allowed regions of the model parameters for the two types are shown numerically for a given region of two combinations of the CP violating phases.