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Simple algebras over local fields

  • André Weil
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 144)

Abstract

Let D be a division algebra of finite dimension over any field K; we will consider left vector-spaces over D, whose dimension will always be assumed finite and <0. If V and W are such spaces, we write Hom(V,W) for the space of homomorphisms of V into W , and let it operate on the right on V; in other words, if a is such a homo-morphism, and vV, we write v α for the image of v under α. We consider Hom(V, W), in an obvious manner, as a vector-space over K; as such, it has a finite dimension, since it is a subspace of the space of K-linear mappings of V into W. As usual, we write End (V) for Hom(V, V).

Keywords

Local Field Haar Measure Division Algebra Compact Subgroup Simple Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1973

Authors and Affiliations

  • André Weil
    • 1
  1. 1.The Institute for Advanced StudyPrincetonUSA

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