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Classification of Subspaces in Spaces with Definite Forms

  • Herbert Gross
Part of the Progress in Mathematics book series (PM, volume 1)

Abstract

In the whole chapter (E, Φ) will be a positive definite hermitean space of dimension אo over the divisionring k with involution ξ ⟼ ξτ. If τ ≠ 1 then it follows from Dieudonné’s lemma that k is either a quadratic extension k = ko (γ) over an ordered field (ko, <) with 0 > γ2 ∈ ko and (x+yγ)τ = x-yγ for all x, y ∈ ko: or k is a quaternion algebra \((\frac{{\alpha ,\beta }} {{{k_0}}})\) with ko ordered, α, β < 0 and τ being the usual “conjugation”. If τ = 1, possible only when k is commutative, then ϕ is symmetric and k = ko is ordered.

Keywords

Standard Basis Orthogonal Group Induction Assumption Hermitean Form Dense Subspace 
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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References to Chapter XII

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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Herbert Gross
    • 1
  1. 1.Mathematisches InstitutUniversität ZürichZürichSwitzerland

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