The C∗-algebra C∗(E) of a directed graph E is generated by partial isometries satisfying relations which reflect the path structure of the graph. In [10], Kumjian and Pask considered the action of a group G on C∗(E) induced by an action of G on E. They proved that if G acts freely and E is locally finite, then the crossed product C∗(E) × G is Morita equivalent to the C∗-algebra of the quotient ...

Let H be a full Hilbert bimodule over a C-algebra A. We show that the Cuntz–Pimsner algebra associated to H is exact if and only if A is exact. Using this result, we give alternative proofs for exactness of reduced amalgemated free products of exact C– algebras. In the case that A is a finite–dimensional C–algebra, we also show that the Brown–Voiculescu topological entropy of Bogljubov automorp...

It is a well-known result of the covering groups that a subgroup G of the fundamental group at the identity of a semilocally simply connected topological group determines a covering morphism of topological groups with characteristic group G . In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We ...

In this paper, pretopological and topological operators are introduced based on partially continuous linear transformations of the membership and non-membership functions for intuitionistic fuzzy sets. They turn out to be a generalization of the topological operators for intuitionistic fuzzy sets.On the other hand it is a generalization of the fuzzy set pretopological operators introduced...

We study the topological centers of $nth$ dual of Banach $mathcal{A}$-modules and we extend some propositions from Lau and "{U}lger into $n-th$ dual of Banach $mathcal{A}-modules$ where $ngeq 0$ is even number. Let   $mathcal{B}$   be a Banach  $mathcal{A}-bimodule$. By using some new conditions, we show that $ Z^ell_{mathcal{A}^{(n)}}(mathcal{B}^{(n)})=mathcal{B}^{(n)}$ and $ Z^ell_{mathcal{B}...

We develop notions of a representation of a topological graph E and of a covariant representation of a topological graph E which do not require the machinery of C∗-correspondences and Cuntz– Pimsner algebras. We show that the C∗-algebra generated by a universal representation of E is isomorphic to the Toeplitz algebra of Katsura’s topological-graph bimodule, and that the C∗-algebra generated by...

A self-dual algebra is an associative or Lie algebra A together with an A bimodule isomorphism A → A∨op, where A∨ = Homk(A, k), the dual bimodule to A (considered as an A bimodule), and A∨op is the the same underlying k module as A∨ but is an A bimodule whose left operation by an element a ∈ A is the same as the right operation by a on A∨, and similarly with left and right interchanged. This in...

Introduction 1 1. Topological AR-quivers 2 2. Theorem of Brady-Watt and Bessis 3 3. Exceptional sequences 4 3.1. Basic definitions 5 3.2. Braid action on exceptional sequences 6 3.3. Example: Auslander-Reiten translation 7 4. Theorems about exceptional sequences 8 5. Appendix 10 5.1. Example: A2 10 5.2. More general almost split sequences 11 5.3. Bimodule of injectives 11 5.4. Untwisting in sep...

A unital Fréchet algebra A is called contractible if there exists an element d ∈ A⊗̂A such that πA(d) = 1 and ad = da for all a ∈ A where πA : A⊗̂A → A is the canonical Fréchet A-bimodule morphism. We give a sufficient condition for an infinite-dimensional contractible Fréchet algebra A to be a direct sum of a finite-dimensional semisimple algebra M and a contractible Fréchet algebra N without an...

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...