Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Μιχάλης Μαλιάκας Καθηγητής
Original Title:
Η ομάδα Brauer και κεντρικές απλές άλγεβρες
Translated title:
The Brauer Group and central simple algebras
Summary:
The purpose of this dissertation is to study the Brauer group. It is proven
that the Brauer group is the union of relative Brauer groups over finite Galois
extensions. Using the notion of the crossed product algebra it can be proven
that each such relative Brauer group is isomorphic to the cohomology group of
order two of the Galois group of the extension. This allows us to answer
questions about the Brauer group by translating them into questions about the
cohomology group. Using this method it can be proven that the Brauer group is
torsion. Moreover, one can prove a structure theorem about central simple
algebras.
Keywords:
Central simple algebras, Brauer Group, Crossed Product Algebras, Cohomology Group, Relative Brauer Group
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