The automorphisms of generalized cyclic Azumaya algebras

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...

Deformations of Azumaya Algebras

In this paper we compute the deformation theory of a special class of algebras, namely of Azumaya algebras on a manifold (C or complex analytic). Deformation theory of associative algebras was initiated by Gerstenhaber in [G]. A deformation of an associative algebra A over an Artinian ring a is an a-linear associative algebra structure on A⊗ a such that, for the maximal ideal m of a, A ⊗ m is a...

Some automorphisms of Generalized Kac-Moody algebras

In this paper we consider some algebraic structures associated to a class of outer automorphisms of generalized Kac-Moody (GKM) algebras. These structures have recently been introduced in [2] for a smaller class of outer automorphisms in the case of ordinary Kac-Moody algebras with symmetrizable Cartan matrices. A GKM algebra G = G(A) is essentially described by its Cartan matrix, A = (aij)i,j∈...

Azumaya algebras and derivations

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...