A general approach to finite-dimensional division algebras

• Autorzy: Ernst Dieterich
• Języki publikacji: EN

Abstrakty

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 ∈ {2,4,8} and the problem of describing their blocks, along with an account of known partial solutions to this problem.

Kategorie tematyczne

• 17A20: Flexible algebras
• 17A30: Algebras satisfying other identities
• 17A45: Quadratic algebras (but not quadratic Jordan algebras)
• 17A80: Valued algebras
• 17A35: Division algebras
• 17B40: Automorphisms, derivations, other operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 126
• Numer: 1
• Strony: 73-86

Daty

wydano

2012

Twórcy

autor

Ernst Dieterich

• Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden

Identyfikatory

DOI

10.4064/cm126-1-4