Classification of Hermitean Forms in Characteristic 2

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.