Simple algebras over local fields

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


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).


Local Field Haar Measure Division Algebra Compact Subgroup Simple Algebra 
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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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