Open AccessOn the classification of finite-dimensional Henselian simple central algebras with unitary involutions
Author(s) -
И. О. Говорушко,
Вячеслав Иванович Янчевский
Publication year - 2020
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2020-56-2-135-143
Subject(s) - mathematics , unitary state , abelian group , pure mathematics , isomorphism (crystallography) , division algebra , simple (philosophy) , invariant (physics) , algebra over a field , algebra representation , mathematical physics , crystallography , chemistry , crystal structure , philosophy , epistemology , political science , law
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 (D 1 , G, (ω, f )) and (D 2 , G, (ϖ, g )), was proven for the case D 1 = D 2 . 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.