Azumaya algebras which are not smash products

Smash Products of Quasi-hereditary Graded Algebras

The Smash product of a finite dimensional quasi-hereditary algebra graded by a finite group with the group is proved to be a quasihereditary algebra. Some elementary relations between the good modules of the two quasi-hereditary algebras are given.

There Are Enough Azumaya Algebras on Surfaces

Using Maruyama’s theory of elementary transformations, I show that the Brauer group surjects onto the cohomological Brauer group for separated geometrically normal algebraic surfaces. As an application, I infer the existence of nonfree vector bundles on proper normal algebraic surfaces.

Antiflexible Algebras Which Are Not Power-associative

Power-associative antiflexible algebras have been studied by the author [3] and Kosier [2]. As a matter of terminology, we shall define an algebra as a finite dimensional vector space on which a multiplication is defined in which both distributive laws are satisfied. If A is an algebra over a field F of characteristic not two, then A has an attached algebra A + which is the same additive group ...

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...