Open Problems on Central Simple Algebras

TL;DR

This paper surveys the current state of research and highlights open problems related to central simple algebras and the Brauer group, aiming to guide future investigations in algebraic structures.

Contribution

It compiles and discusses unresolved questions in the theory of central simple algebras and the Brauer group, serving as a resource for researchers and newcomers.

Findings

Identifies key open problems in the field.

Summarizes existing research on central simple algebras.

Provides a comprehensive overview for future work.

Abstract

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.