A Survey of the Classification of Division Algebras
Abstract
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.
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Michelle Roshan Marie Ashburner
(2008).
A Survey of the Classification of Division Algebras. UWSpace.
http://hdl.handle.net/10012/4072
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