Classification of Hermitean Forms in Characteristic 2

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


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.


Orthogonal Basis Hyperbolic Plane Hermitean Form Additive Subgroup Degenerate Part 
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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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