A central result here is the computation of the entire cyclic homology of canonical smooth subalgebras of stable continuous trace C∗-algebras having smooth manifolds M as their spectrum. More precisely, the entire cyclic homology is shown to be canonically isomorphic to the continuous periodic cyclic homology for these algebras. By an earlier result of the authors, one concludes that the entire...

We study some topological properties of maximal ideal spaces of certain algebras of almost periodic functions. Our main result is that such spaces are contractible. We present several analytic corollaries of this result. MSC: 42A75; 46J10

We define and study twisted support varieties for modules over an Artin algebra, where the twist is induced by an automorphism of the algebra. Under a certain finite generation hypothesis we show that the twisted variety of a module satisfies Dade’s Lemma and is one dimensional precisely when the module is periodic with respect to the twisting automorphism. As a special case we obtain results o...

The finite-dimensional symmetric algebras over algebraically closed fields, based on surface triangulations, motivated by the theory of cluster algebras, have been extensively investigated and applied. In particular, weighted their deformations were introduced studied in [14], [15], [16], [17], [18], it was shown that all these except a few singular cases, are tame periodic period 4. this artic...

It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener–Hopf typ...

We construct canonical integral transforms, analogous to the Fourier transform, that have periods six and three. The existence of this transform is shown to arise naturally from the expectation that the Schwartz space on the real line, viewed as the Heisenberg module of Rieffel and Connes over the rotation C*-algebra, should extend to a module action over the crossed product of the latter by th...

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. We describe how radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Li...

We study weight posets of weight multiplicity free (WMF) representations of reductive Lie algebras. Specifically, we are interested in relations between dimR and the number of edges in the Hasse diagram of the corresponding weight poset #E(R). We compute the number of edges and upper covering polynomials for the weight posets of all WMFrepresentations. We also point out non-trivial isomorphisms...