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A general approach to finite dimensional division algebras
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2011 (English)Report (Other academic)
Abstract [en]

We present a short and rather self-contained introduction to the theory of finite dimensional division algebras, setting out from the basic definitions and leading up to recent results and current directions of research. In sections 2-3 we develop the general theory over an arbitrary ground field k, with emphasis on the trichotomy of fields imposed by the dimensions in which a division algebra exists, the groupoid structure of the level subcategories Dn(k), and the role played by the irreducible morphisms. Sections 4-5 deal with the classical case of real division algebras, emphasizing the double sign decomposition of the level subcategories Dn(R) for n E {2, 4, 8} and the problem of describing their blocks, along with an account of known partial solutions to this problem.

Place, publisher, year, edition, pages
2011. , 15 p.
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 2011:20
Keyword [en]
Division algebra, groupoid, irreducible morphism, double sign decomposition, description of blocks
National Category
Algebra and Logic
Research subject
URN: urn:nbn:se:uu:diva-160648OAI: diva2:452170
Available from: 2011-10-28 Created: 2011-10-28 Last updated: 2012-02-16Bibliographically approved

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