On the classification of finite-dimensional Henselian simple central algebras with unitary involutions
https://doi.org/10.29235/1561-2430-2020-56-2-135-143
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.
About the Authors
I. O. Govorushko
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Igor O. Govorushko – Ph. D. (Physics and Mathematics), Researcher of the Department of Algebra
11, Surganov Str., 220072, Minsk
V. I. Yanchevskii
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Vyacheslav I. Yanchevskii – Academician of the National Academy of Sciences of Belarus, Dr. Sc. (Physics and Mathematics), Professor, Head of the Department of Algebra
11, Surganov Str., 220072, Minsk
References
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