Abstract
The purpose of this paper is to investigate the problem of the classification of finite-dimensional simple central K-algebras with unitary involutions. In this paper, K-isomorphism is proven for weakly ramified finite-dimensional central K-algebras with division and unitary K/k-involutions (where the invariant field k is Henselian). Earlier, in papers by J.-P. Tignol, V. V. Kursov and V. I. Yanchevskii, generalized Abelian crossed products were defined and the K-isomorphism of generalized Abelian crossed products (D1, G, (ω, f )) and (D2, G, (ϖ, g )), was proven for the case D1 = D2. In this paper, this criterion is proven when D1 and D2 are different. With the help of this criterion, the main result of this article is obtained.
Highlights
Продолжение нормирования v на D будем обозначать также через v
Приняв t(ζ) равным 1 для всех ζ ∈G, получаем, что обобщенные 2-коциклы (ω, f ) и (ω , g) когомологичны
Summary
Такие алгебры называются F-изоморфными, если существует F-изоморфизм σ : A1 → A2 алгебр A1 и A2 такой, что диаграмма Существует такой автоморфизм ω(ξ) ∈G , что ω(ξ) |Z = ξ для любого ξ ∈G. Известно [1, теорема 1.3], что обобщенные абелевы скрещенные произведения ( D1,G,(ω, f )) и ( D1,G,(ω ′, g′)) = ξ⊕∈G D1x ξ (где ω ′(ξ) = χ −1 ⋅ ω (ξ) ⋅ χ для всех ξ ∈G и g′(ξ,η)= g(ξ,η)χ для всех ξ,η∈G) K-изоморфны.
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