We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

In this paper, we compute the Laplacian spectrum of non-commuting graphs of some classes of finite non-abelian groups. Our computations reveal that the non-commuting graphs of all the groups considered in this paper are L-integral. We also obtain some conditions on a group G so that its non-commuting graph is L-integral.

We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower Q ⊂ K ⊂ L forces the tower to be split in a very strong sense.

The path integral for 3+1 abelian gauge theory is rewritten in terms of a real antisymmetric field allowing a dual action that couples the electric and magnetic currents to the photon and each other in a gauge invariant manner. Standard perturbative abelian quantum electrodynamics reemerges when the monopole current vanishes. For certain simple relationships between the monopole current and the...

In this short review main issues related to the non-Abelian Stokes theorem have been addressed. The two principal approaches to the non-Abelian Stokes theorem, operator and two variants (coherent-state and holomorphic) of the path-integral one, have been formulated in their simplest possible forms. A recent generalization for a knotted loop as well as a suggestion concerning higher-degree forms...

The Lie-Poisson structure of non-Abelian Thirring models is discussed and the Hamiltonian quantization of these theories is carried out. The consistency of the Hamiltonian quantization with the path integral method is established. It is shown that the space of non-Abelian Thirring models contains the nonperturbative conformal points which are in one-to-one correspondence with general solutions ...

Simulation of an Abelian Higgs theory in world line (polymer) representation. In World Line Path Integral representation Abelian Higgs theories admit a curvature term in the Hamiltonian. Using Monte Carlo simulations we show that the curvature term drives a phase transition at sufficiently strong coupling. In quenched approximation this phase transition is smooth, with implications that the mod...

We give a formulation of the abelian case of Stark’s Main Conjecture in terms of determinants of projective modules and briefly show how this formulation leads naturally to its Equivariant Tamagawa Number Conjecture (ETNC) – type integral refinements. We discuss the Rubin-Stark integral refinement of an idempotent p1 iece of Stark’s Abelian Main Conjecture. In the process, we give a new formula...

This paper is a survey of results obtained by the present author towards proving Rubin’s integral version of Stark’s conjecture for abelian L– functions of arbitrary order of vanishing at the origin. Rubin’s conjecture is stated and its links to the classical integral Stark conjecture for L–functions of order of vanishing 1 are discussed. A weaker version of Rubin’s conjecture formulated by the...

Title of thesis: CLASSIFICATION OF PRIME IDEALS IN INTEGRAL GROUP ALGEBRAS OF FINITE ABELIAN GROUPS Heather Mallie McDonough, Master of Arts, 2005 Thesis directed by: Professor William Adams Department of Mathematics Let Z[G] be the integral group algebra of the group G. In this thesis, we consider the problem of determining all prime ideals of Z[G] where G is both finite and abelian. Because o...