The multiplicative group of a global field acts on its adele ring by multiplication. We consider the crossed product algebra of the resulting action on the space of Schwartz functions on the adele ring and compute its Hochschild, cyclic and periodic cyclic homology. We also compute the topological K-theory of the C-algebra crossed product.

In this paper we describe the commutant of an arbitrary subalgebra A of the algebra of functions on a set X in a crossed product of A with the integers, where the latter act on A by a composition automorphism defined via a bijection of X . The resulting conditions which are necessary and sufficient for A to be maximal abelian in the crossed product are subsequently applied to situations where t...

In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.

In this paper we investigate the interrelation between the topological freedom of partial actions of discrete groups and faithful representations of partial crossed products

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.

Given a finite dimensional algebra A of finite global dimension, we consider the trivial extension of A by the A − A-bimodule ⊕i≥2 Ext 2 A(DA,A), which we call the higher relation bimodule. We first give a recipe allowing to construct the quiver of this trivial extension in case A is a string algebra and then apply it to prove that, if A is gentle, then the tensor algebra of the higher relation...

We construct a constant depth quantum circuit that maps between Morita-equivalent string-net models. Due to its and unitarity, the cannot alter topological order, which demonstrates string nets are in same phase. The is constructed from an invertible bimodule category connecting two input fusion categories of relevant models, acting as generalized Fourier transform for categories. not only acts...