This paper explores the effect of various graphical constructions upon the associated graph C∗-algebras. The graphical constructions in question arise naturally in the study of flow equivalence for topological Markov chains. We prove that outsplittings give rise to isomorphic graph algebras, and in-splittings give rise to strongly Morita equivalent C∗-algebras. We generalise the notion of a del...

We consider two categories of C-algebras; in the first, the isomorphisms are ordinary isomorphisms, and in the second, the isomorphisms are Morita equivalences. We show how these two categories, and categories of dynamical systems based on them, crop up in a variety of C-algebraic contexts. We show that Rieffel’s construction of a fixed-point algebra for a proper action can be made into functor...

Based on the usual Fedosov construction of star products for a symplectic manifold M we give a simple geometric construction of a bimodule deformation for the sections of a vector bundle over M starting with a symplectic connection on M and a connection for E. In the case of a line bundle this gives a Morita equivalence bimodule where the relation between the characteristic classes of the Morit...

By a theorem due to Kato and Ohtake, any (not necessarily strict) Morita context induces an equivalence between appropriate subcategories of the module categories of the two rings in the Morita context. These are in fact categories of firm modules for non-unital subrings. We apply this result to various Morita contexts associated to a comodule Σ of an A-coring C. This allows to extend (weak and...

Categorical aspects of the theory modules over trusses are studied. Tensor product is defined and its existence established. In particular, it shown that bimodules form a monoidal category. Truss versions Eilenberg-Watts theorem Morita equivalence formulated. Projective small-projective their properties

We answer a question of Blecher--Muhly--Paulsen, identifying topological invariants for cb Morita equivalences holomorphic cross-section algebras. Previously, given certain subcontext context n-homogeneous C?-algebras whose spectrum T is an annulus, the norm lifting 1A subalgebra A was estimated by conformal and bundle invariants. give generalization in which bordered Riemann surface. In doing ...