An action of Z by automorphisms of a k-graph induces an action of Z by automorphisms of the corresponding k-graph C∗-algebra. We show how to construct a (k + l)-graph whose C∗-algebra coincides with the crossed product of the original k-graph C∗-algebra by Z. We then investigate the structure of the crossed-product C∗-algebra.

We introduce a notion of covering dimension for Cuntz semigroups C⁎-algebras. This is always bounded by the nuclear C⁎-algebra, and subhomogeneous C⁎-algebras both dimensions agree. Z-stable have at most one. Further, semigroup simple, C⁎-algebra zero-dimensional if only has real rank zero or stably projectionless.

A pro-C∗-algebra is a (projective) limit of C∗-algebras in the category of topological ∗algebras. From the perspective of non-commutative geometry, pro-C∗-algebras can be seen as non-commutative k-spaces. An element of a pro-C∗-algebra is bounded if there is a uniform bound for the norm of its images under any continuous ∗-homomorphism into a C∗-algebra. The ∗-subalgebra consisting of the bound...

in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).