We prove that for every group G and any two sets I, J , the Brandt semigroup algebras l(B(I,G)) and l(B(J,G)) are Morita equivalent with respect to the Morita theory of selfinduced Banach algebras introduced by Grønbæk. As applications, we show that if G is an amenable group, then for a wide class of Banach l(B(I,G))-bimodules E, and every n > 0, the bounded Hochschild cohomology groups H(l(B(I...

We consider the variety G2,p of nilpotent groups of class 2 of exponent p > 2 in the language L of group theory. To get the Amalgamation Property (AP) in [Bau] an additional predicate P (G) for G ∈ G2,p with G ′ ⊆ P (G) ⊆ Z(G) is introduced. Let GP2,p be the category of this groups in the extended language LP where the morphisms are embeddings. Using the class KP2,p of finite structures in GP2,...

In this paper, we study the Plancherel measure of a class of non-connected nilpotent groups which is of special interest in Gabor theory. Let G be a time-frequency group. That is G = ⟨ Tk,Ml : k ∈ Z, l ∈ BZ ⟩ , where Tk, Ml are translations and modulations operators acting in L(R), and B is a non-singular matrix. We compute the Plancherel measure of the left regular representation of G which is...

We study the question of surjectivity Galois correspondence from subHopf algebras to subfields given by Fundamental Theorem Theory for abelian Hopf structures on a extension fields with group G', finite p-group. Applying connection between regular subgroups holomorph p-group (G, +) and associative, commutative nilpotent algebra A Caranti, et. al., we show that if gives rise H-Hopf structure L/K...

Dr. George Lush Foss who died on 11th February 1985 at the age of 76 years was not only a highly respected General Practitioner in Bristol but also a pioneer in the early days of Endocrinology and the problems of sub-fertility. Educated at Marlborough and Jesus College, Cambridge he did his clinical training in Bristol where his father was a general practitioner in St. George. On the very day t...

The K-theory of the title is described in terms of the Ktheory of finite subgroups, as generalized sheaf homology of a quotient space. A corollary is that if G is torsion-free, then the Whitehead groups Wh t(ZG) vanish for all i. 1. The main result. Suppose that G is a poly-(finite or cyclic) group. Then there is a virtually connected and solvable Lie group L that contains G as a discrete cocom...

Introduction. Voiculescu’s theory of freeness in noncommutative probability spaces (see [10,11,12,13,14,15], especially the latter for an overview) has made possible the recent surge of results about and related to the free group factors L(Fn) [13,3,7,8,9,4]. One hopes to eventually be able to solve the old isomorphism question, first raised by R.V. Kadison in the 1960’s, of whether L(Fn) ∼= L(...