Let F be a Henselian valued field with char(F ) = p and D a semi-ramified, “not strongly degenerate” p-algebra. We show that all Galois subfields of D are inertial. Using this as a tool we study generic abelian crossed product p-algebras, proving among other things that the noncyclic generic abelian crossed product p-algebras defined by non-degenerate matrices are indecomposable p-algebras. To ...

We define the tracial Rokhlin property for actions of finite cyclic groups on stably finite simple unital C*-algebras. We prove that the crossed product of a stably finite simple unital C*-algebra with tracial rank zero by an action with this property again has tracial rank zero. Under a kind of weak approximate innerness assumption and one other technical condition, we prove that if the action...

The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C∗-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting. First, we show that if G is an amenable groupoid acting on an upper-semicontinuous C∗-bundle A with nuclear section algebra A, then the associated g...

Given a partial action α of a group G on an associative algebra A, we consider the crossed product A α G. Using the algebras of multipliers, we generalize a result of Exel (1997) on the associativity of A α G obtained in the context of C∗-algebras. In particular, we prove that A αG is associative, provided that A is semiprime. We also give a criterion for the existence of a global extension of ...

We show that the category A(G) of actions of a locally compact group G on C∗-algebras (with equivariant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C∗(G), δG); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma category of norm...

We study a notion of residual finiteness for continuous actions of discrete groups on compact Hausdorff spaces and how it relates to the existence of norm microstates for the reduced crossed product. Our main result asserts that an action of a free group on a zero-dimensional compact metrizable space is residually finite if and only if its reduced crossed product admits norm microstates, i.e., ...

We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov pro...

Given D a commutative Noetherian domain and G a finite group acting faithfully on D as automorphisms of D, we describe the Azumaya locus of the crossed product D ∗ G and relate it with the singular locus of DG. To achieve this we will impose some basic homological conditions on D and on D ∗ G. Also, we give necessary and suficient conditions for a crossed product to be Azumaya.

We demonstrate that the perforative phenomena shown to occur among simple amenable C∗-algebras by Villadsen and Toms can be realized within a dynamical framework. More specifically, we construct a minimal homeomorphism for which the K0 group of the crossed product fails to be weakly unperforated, and a minimal homeomorphism for which the crossed product has the same Elliott invariant as an AT-a...

For a twisted partial action Θ of a group G on an (associative nonnecessarily unital) algebra A over a commutative unital ring k, the crossed product A⋊ΘG is proved to be associative. Given a G-graded k-algebra B = ⊕g∈GBg with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B1⋊ΘG for some twisted partial action of G on ...