A Survey of the Classification of Division Algebras

Division Algebra;Central Simple Algebra;Crossed Product;PI Algebra;Growth;Pure Mathematics

Ashburner, Michelle Roshan Marie

University of Waterloo

关键词: Division Algebra;    Central Simple Algebra;    Crossed Product;    PI Algebra;    Growth;    Pure Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/4072/1/MAthesis3.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

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.