Brauer groups of fields and quaternion algebras

Stratou, Nefeli (2021) Brauer groups of fields and quaternion algebras. Bachelor's Thesis, Mathematics.

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Abstract

The definition of the Brauer group of a field k arose in the attempt of classifying finite dimensional central division k-algebras. Indeed, the elements in the Brauer group are classes of finite dimensional central simple k-algebras under a suitable equivalence relation, and Wedderburn's theorem gives a bijection between these classes and the finite dimensional central division k-algebras (up to isomorphism). The Brauer group is an abelian group and its operation is induced by the tensor product. While the Brauer group of certain fields (e.g. any algebraically closed or finite field) is trivial, the Brauer group of Q is more complicated. In this project, we focus on its subgroup formed by elements of order dividing two. In particular, quaternion algebras are examples of central simple k-algebras giving rise to elements in this subgroup; by investigating their properties thoroughly, we perform some explicit computations in the Brauer group.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Bianchi, F. and Muller, J.S.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	27 May 2021 09:48
Last Modified:	27 May 2021 09:49
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/24455

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