We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona type theorems, properties of divisors, holomorphic analogs of the Peter-Weyl approximation theorem, Hartogs type theorems, characterization of uniqueness sets. The model examples ...

Determinant formulae are presented for the periodic, antiperiodic and twisted N = 2 superconformal algebras in two dimensions, and a classification is derived of the unitary highest weight representations. Physical realisations of several of these representations are discussed. In particular, it is noted that the unitarity constraints apply to string compactification, giving results which are n...

Kumjian and Pask introduced an aperiodicity condition for higher rank graphs. We present a detailed analysis of when this occurs in certain rank 2 graphs. When the algebra is aperiodic, we give another proof of the simplicity of C(Fθ ). The periodic C*algebras are characterized, and it is shown that C(Fθ ) ' C(T)⊗A where A is a simple C*-algebra.

We develop a theory of almost periodic elements in Banach algebras and present an abstract version of a noncommutative Wiener’s Lemma. The theory can be used, for example, to derive some of the recently obtained results in time-frequency analysis such as the spectral properties of the finite linear combinations of time-frequency shifts.

An extension of bornological algebras with a bounded linear section gives rise to a six term exact sequence of the associated periodic and entire cyclic cohomology groups. 1. Introduction A convex vector bornology on a vector space is a collection of subsets satisfying some conditions 8]. A typical example is the collection of bounded subsets of a locally convex vector space. A bornological alg...

A Fréchet algebra endowed with a multiplicatively convex topology has two types of invariants: homotopy invariants (topological K-theory and periodic cyclic homology) and secondary invariants (multiplicative Ktheory and the non-periodic versions of cyclic homology). The first aim of this paper is to establish a Riemann-Roch-Grothendieck theorem which describes direct images for homotopy and sec...

We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the q → 1 limit of the q-deformed affine ŝl(2) symmetry of the sine-Gordon theory, this limit occurring at the free fermion point. Working in radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Lie alg...

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 prove that certain free products of factors of type I and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki-Woods factors. In particular, they have the free absorption property and Connes’ Sd invariant completely classifies these free products. For example, for λ, μ ∈]0, 1[, we show that (M2(C), ωλ) ∗ (M2(C), ωμ) is isomorphic to the...

We review topologically Nistor’s computation of the homogeneous part of the periodic cyclic cohomology of crossed products Γ⋉A of torsion-free discrete groups Γ with a complex Γ-algebra A. We use periodic cyclic cohomology associated to bornological algebras. Let G be a complex connected semisimple Lie group and B be a minimal parabolic subgroup of G. Applied to torsion-free discrete subgroups ...