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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.
2012 (English)In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 126, no 1, 73-86 p.Article in journal (Refereed) Published
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 D-n(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 D-n(R) for n is an element of {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
2012. Vol. 126, no 1, 73-86 p.
National Category
Algebra and Logic
URN: urn:nbn:se:uu:diva-173442DOI: 10.4064/cm126-1-4ISI: 000303077300004OAI: oai:DiVA.org:uu-173442DiVA: diva2:517662
Available from: 2012-04-24 Created: 2012-04-24 Last updated: 2012-05-22Bibliographically approved

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