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Classification of Hermitean Forms in Characteristic 2

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

Abstract

All forms considered in this chapter are e-hermitean forms over a field k of characteristic 2 equipped with antiautomorphism ξ⟼ ξ*. In k we consider the additive subgroups S ≔ {α ∈ k|α = εα*} and T ≔ {α + εα*|α ∈ k} of “symmetric” elements and of “traces” respectively. The factor group S/T is a k-left vectorspace under the composition λ (σ+T) = λσλ* + T (σ ∈ S, λ ∈ k). ̂: S → S/T is the canonical map.

Keywords

Orthogonal Basis Hyperbolic Plane Hermitean Form Additive Subgroup Degenerate Part 
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 VII

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    F. Ayres, The expression of non-singular row-finite matrices in terms of strings. Ann. Univ.Sci. Budapest. Sectio Math. 7 (1964) 91–96.Google Scholar
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    H. Gross and R.D. Engle, Bilinear forms on k-vector spaces of denumerable dimension in the case of char(k) = 2, Comment. Math.Helv. 40 (1965) 247–266.CrossRefGoogle Scholar
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    G. Maxwell, Classification of countably infinite hermitean forms over skewfields. Amer. J. Math. 96 (1974) 145–155.CrossRefGoogle Scholar
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    J. Milnor, Symmetric inner products in characteristic 2. In “prospects in Mathematics” Ann. of Math. Studies, No. 70 Princeton Univ. Press 59–75.Google Scholar
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    P. Vermes, Multiplicative groups of row- and column-finite infinite matrices. Ann. Univ. Sci. Budapest, Sectio Math. 5 (1962) 15–23.Google Scholar

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

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

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