Central simple algebras as twisted forms of matrix algebras
In this video, I introduce the notion of central simple algebras, of which Hamilton's quaternions are an example. These will then be viewed as "twisted forms" of matrix algebras, just as vector bundles on a topological space X are twisted forms of a trivial bundle X x V where V is a finite dimensional vector space. I explain how this works, as well as how to recover a central simple algebra by using a Galois action on the matrix algebra. This is in complete analogy with building a vector bundle from its trivialisation using transition functions.