In this section we shall assume that all algebras are finite dimensional algebras over an algebraically closed field F. The fact that F is algebraically closed is only for convenience, to avoid the division rings that could arise in the decomposition of Ā just before (4.8) below. Let A ⊆ B be an inclusion of algebras. Then B⊗F B is an (A,A)-bimodule where A acts on the left by left multiplicati...

Let A be a separable unital C*-algebra and let π : A → L(H) be a faithful representation of A on a separable Hilbert space H such that π(A) ∩ K(H) = {0}. We show that OE , the Cuntz-Pimsner algebra associated to the Hilbert A-bimodule E = H⊗C A, is simple and purely infinite. If A is nuclear and belongs to the bootstrap class to which the UCT applies, then the same applies to OE . Hence by the ...

Let X be a Hilbert bimodule over a C-algebra A and OX = A ⋊X Z. Using a finite section method we construct a sequence of completely positive contractions factoring through matrix algebras over A which act on sξs ∗ η as Schur multipliers converging to the identity. This shows immediately that for a finitely generated X the algebra OX inherits any standard approximation property such as nuclearit...

Mackey’s imprimitivity theorem characterises the unitary representations of a locally compact group G which have been induced from representations of a closed subgroupK; Rieffel’s influential reformulation says that the group C-algebra C(K) is Morita equivalent to the crossed product C0(G/K) × G [14]. There have since been many important generalisations of this theorem, especially by Rieffel [1...

In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

We have introduced a notion of C∗-symbolic dynamical system in [K. Matsumoto: Actions of symbolic dynamical systems on C∗-algebras, to appear in J. Reine Angew. Math.], that is a finite family of endomorphisms of a C∗-algebra with some conditions. The endomorphisms are indexed by symbols and yield both a subshift and a C∗-algebra of a Hilbert C∗-bimodule. The associated C∗-algebra with the C∗-s...

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...

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type Ã. 2000 Mathematics Subject Classification : 16E40

One of the purposes in the computation of cohomology groups is to establish invariants which may be helpful in the classification of the objects under consideration. In the theory of continuous Hochschild cohomology for operator algebras R. V. Kadison and J. R. Ringrose proved [10] that for any hyperfinite von Neumann algebra M and any dual normal M-bimodule S, all the continuous cohomology gro...