Questions tagged [azumaya-algebras]
A generalization of central simple algebras over arbitrary commutative rings, or over a scheme
4
questions
6
votes
1answer
209 views
Category of modules over an Azumaya algebra and the Brauer group
Let $k$ be a field, and let $\alpha \in \mathrm{Br}(k)$. Let $A$ be an Azumaya algebra representing $\alpha$. Then the category $A$–$\mathrm{mod}$ depends only on $\alpha$.
I would like to know ...
5
votes
0answers
78 views
Hochschild cohomology of an Azumaya algebra
Let $k$ be a field. Given a commutative $k$-algebra $Z$ and an associative algebra $A$ that is Azumaya over $Z$, do we have an isomorphism of Hochschild cohomologies: $HH^*(A) \cong HH^*(Z)$?
This is ...
2
votes
1answer
482 views
Are differential forms related to Azumaya algebras?
While studying vector bundle valued differential forms, $\Omega^{\bullet}(M, E)$, or $\Omega^{\bullet}(M, \mathrm{End}(E))$ if that helps this discussion, I've come across some work in Azumaya ...
5
votes
1answer
262 views
An example of an Azumaya algebra that isn't free over its centre
Azumaya originally defined an Azumaya algebra (which he called a proper maximally central algebra) to be an algebra A which is a free module of finite rank over its centre Z such that the natural map
$...
