We classify the finite semigroups S, for which all Z-orders Γ of QS, the unit group U(Γ) is hyperbolic. We also classify the RA-loops L for which the unit loop of its integral loop ring does not contain any free abelian subgroup of rank two.

We introduce an integral version of the Eisenstein cocycle. As applications we prove a conjecture of Gross regarding the “order of vanishing” of Stickelberger elements relative to an abelian tower of fields and give a cohomological construction of the conjectural Gross–Stark units.

We present a new method of formulating the classical theory of SU(N + 1) non-Abelian Chern-Simons (NACS) particles for arbitrary N ≥ 1 using the symplectic reduction of CP (N) manifold from S2N+1. Quantizing the theory using BRST formulation and coherent state path integral method , we obtain a quantum mechanical model for SU(N + 1) NACS particles.

Integral formulae for form factors of a large family of charged local operators in SU(2) invariant Thirring model are given extending Smirnov’s construction of form factors of chargeless local operators in the sine-Gordon model. New abelian symmetry acting on this family of local operators is found. It creates Lukyanov’s operators which are not in the above family of local operators in general.

We compute the cohomology of the subgroup of the integral symplectic group of degree 2 consisting of matrices γ ≡ 1 mod 4. This is done by computing the cohomology of the moduli space of principally polarized abelian surfaces with a level 4 structure. This space has a projective smooth compactification whose topology was analyzed by Lee and Weintraub in a recent work.

In this note we use a functional approach to the integral to obtain a special case of the Keisler-Fubini theorem; the general case can be obtained with a similar proof. An immediate appUcation is the standard Fubini theorem for products of Radon measures. Similar methods give the Weil formula for quotient groups of compact Abelian groups.

In this paper, we complete the classification of those finite 3groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that Z[G] satisfies MJD. In the nonabelian case, we show that Z[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27.

In this article we shall give a survey of Hasse’s problem for integral power bases of algebraic number fields during the last half of century. Specifically, we developed this problem for the abelian number fields and we shall show several substantial examples for our main theorem [7] [9], which will indicate the actual method to generalize for the forthcoming theme on Hasse’s problem [15].

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. We show that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory.