Let X be an infinite compact metric space with finite covering dimension and let h : X → X be a minimal homeomorphism. We show that the associated crossed product C*-algebra A = C∗(Z, X, h) has tracial rank zero whenever the image of K0(A) in Aff(T (A)) is dense. As a consequence, we show that these crossed product C*-algebras are in fact simple AH algebras with real rank zero. When X is connec...

Consider a projective limit G of finite groups Gn. Fix a compatible family δn of coactions of the Gn on a C ∗-algebra A. From this data we obtain a coaction δ of G on A. We show that the coaction crossed product of A by δ is isomorphic to a direct limit of the coaction crossed products of A by the δn. If A = C∗(Λ) for some k-graph Λ, and if the coactions δn correspond to skewproducts of Λ, then...

The notions of a cleft extension and a cross product with a Hopf algebroid are introduced and studied. In particular it is shown that an extension (with a Hopf algebroid H = (HL,HR)) is cleft if and only if it is HR-Galois and has a normal basis property relative to the base ring L of HL. Cleft extensions are identified as crossed products with invertible cocycles. The relationship between the ...

We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian stabilizers and a well behaved orbit space. In this case, the spectrum of the crossed product is homeomorphic, via an induction map, to a quotient of the spe...

Throughout this paper, k is a field, R is an algebra over k, and H is a Hopf algebra over k. We say that R# σ H is the crossed product of R and H if R# σ H becomes an algebra over k by multiplication: (a#h)(b#g) = h,g a(h 1 · b)σ(h 2 , g 1)#h 3 g 2 Let lpd(R M), lid(R M) and lf d(R M) denote the left projective dimension, left injective dimension and left flat dimension of left R-module M, resp...