A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine integral quartic Cayley graphs on finite abelian groups. As a side result we show that there are exactly 27 connected integral Cayley graphs up to 11 vertices.

We study the density of integral points on punctured abelian surfaces. Linear growth rates are observed experimentally.

We offer an elementary proof of Pontryagin duality theorem for compact and discrete abelian groups. To this end we make use of an elementary proof of Peter-Weyl theorem due to Prodanov that makes no recourse to Haar integral. As a long series of applications of this approach we obtain proofs of Bohr von Neumann’s theorem on almost periodic functions, Comfort-Ross’ theorem on the description of ...

We consider the Wess-Zumino-Witten theory to obtain the functional integral bosonization of the Thirring-Wess model with an arbitrary regularization parameter. Proceeding a systematic of decomposing the Bose field algebra into gauge-invariantand gauge-noninvariant field subalgebras, we obtain the local decoupled quantum action. The generalized operator solutions for the equations of motion are ...

Using algebraic and topological K-theory together with complex C∗-algebras, we prove that every abelian group may be realized as the centre of a strongly torsion generated group whose integral homology is zero in dimension one and isomorphic to two arbitrarily prescribed abelian groups in dimensions two and three.

It has been conjectured that the Abelian projection of QCD is responsible for the confinement of color. Using a gauge independent definition of the Abelian projection (which does not employ any gauge fixing) we prove the Abelian dominance. In specific we prove that the gauge field configuration which contributes to the Wilson loop integral is precisely the gauge covariant part of the restricted...

In this article we construct free groups and subgroups of finite index in the unit group of the integral group ring of a finite non-abelian group G for which every non-linear irreducible complex representation is of degree 2 and with commutator subgroup G′ a central elementary abelian 2-group.

This paper gives an algebraic characterization of expansive actions of countable abelian groups on compact abelian groups. This naturally extends the classification of expansive algebraic Zd-actions given by Schmidt using complex varieties. Also included is an application to a natural class of examples arising from unit subgroups of integral domains. 2000 Mathematics Subject Classification: 22D...

We discuss Abelian and non-Abelian three dimensional bosoniza-tion within the path-integral framework. We present a systematic approach leading to the construction of the bosonic action which, together with the bosonization recipe for fermion currents, describes the original fermion system in terms of vector bosons.