A Survey of the Classification of Division Algebras
MetadataShow full item record
For a given field F we seek all division algebras over F up to isomorphism. This question was first investigated for division algebras of finite dimension over F by Richard Brauer. We discuss the construction of the Brauer group and some examples. Crossed products and PI algebras are then introduced with a focus on Amitsur's non-crossed product algebra. Finally, we look at some modern results of Bell on the Gelfand-Kirillov dimension of finitely generated algebras over F and the classification of their division subalgebras.
Cite this work
Michelle Roshan Marie Ashburner (2008). A Survey of the Classification of Division Algebras. UWSpace. http://hdl.handle.net/10012/4072