In this paper we show that a strongly homotopy commutative (or C∞-) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-algebra (an ∞-generalisation of a commutative Frobenius algebra introduced by Kontsevich). This result relies on the algebraic Hodge decomposition of the cyclic Hochschild cohomology of a C∞-algebra and does not generalize to a...

We associate reduced and full C*-algebras to arbitrary rings and study the inner structure of these ring C*-algebras. As a result, we obtain conditions for them to be purely infinite and simple. We also discuss several examples. Originially, our motivation comes from algebraic number theory.

Develops tools to handle C*-algebras arising as completions of convolution algebras sections line bundles over possibly non-Hausdorff groupoids.

Pure infiniteness (in sense of [11]) is considered for C∗-algebras arising from singly generated dynamical systems. In particular, Cuntz-Krieger algebras and their generalizations, i.e., graph-algebras and OA of an infinite matrix A, admit characterizations of pure infiniteness. As a consequence, these generalized Cuntz-Krieger algebras are traceless if and only if they are purely infinite. Als...

The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([17]) Ando-Kirchberg ([2]). In this paper we give a complete answer to their question: A C*-algebra has algebra if only satisfies Fell's condition. contrast, show that any non-trivial extension compact operators not non-abelian but even residually type I algebra. particular its...

Given a ternary relation C on a set U and an algebra A, we present a construction of a convolution algebra A(U,C) of U = (U,C) over A. This generalises bothmatrix algebras and algebras obtained from convolution of monoids. To any class of algebras corresponds a class of convolution structures. Our study cases are the classes of commutative, associative, Lie, and Jordan algebras. In each of thes...

For certain graphs, we can associate a universal C*-algebra, which encodes the information of the graph algebraically. In this paper we examine the relationships between products of graphs and their associated C*-algebras. We present the underlying theory of associating a C*-algebra to a direct graph as well as to a higher rank graph. We then provide several isomorphisms relating C*-algebras of...

This paper concerns classifying completely positive maps between certain C*-algebras. Several invariants for are constructed. It is proved that one of them isomorphic to the Ext-group C*-algebra extensions in special circumstances. Furthermore, this invariant induces a functor from C*-algebras abelian groups which split-exact.

We prove an analogue of Voiculescu’s theorem: Relative bicommutant of a separable unital subalgebra A of an ultraproduct of simple unital C*-algebras is equal to A. Ultrapowers1 AU of separable algebras are, being subject to well-developed model-theoretic methods, reasonably well-understood (see e.g. [9, Theorem 1.2] and §2). Since the early 1970s and the influential work of McDuff and Connes c...