Generalized crossed products and Azumaya algebras

On the Azumaya Locus of Some Crossed Products

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.

Azumaya algebras and derivations

Motives of Azumaya Algebras

We study the slice filtration for the K-theory of a sheaf of Azumaya algebras A, and for the motive of a Severi-Brauer variety, the latter in the case of a central simple algebra of prime degree over a field. Using the Beilinson-Lichtenbaum conjecture, we apply our results to show the vanishing of SK2(A) for a central simple algebra A of square-free index (prime to the characteristic). This pro...

Azumaya Algebras and Canonical Components

Let M be a compact 3-manifold and Γ = π1(M). The work of Thurston and Culler–Shalen established the SL2(C) character variety X(Γ) as fundamental tool in the study of the geometry and topology of M . This is particularly so in the case when M is the exterior of a hyperbolic knot K in S. The main goals of this paper are to bring to bear tools from algebraic and arithmetic geometry to understand a...

Full Crossed Products by Hopf C∗-algebras

We show that when a co-involutive Hopf C *-algebra S coacts via δ on a C *-algebra A, there exists a full crossed product A × δ S, with universal properties analogous to those of full crossed products by locally compact groups. The dual Hopf C *-algebra is then defined byˆS := C × id S.