##  [Brauer Group](/brauer-group) 

  ##  [Brauer Group](https://algebra.quantumdictionary.io/brauer-group-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The group classifying equivalence classes of central simple algebras over a field (or Azumaya algebras over a scheme), often described cohomologically as H^2 of the multiplicative group in the étale or Galois context; it captures obstructions to splitting algebras and contributes to arithmetic and geometric invariants of varieties.