[图书][B] Value functions on simple algebras, and associated graded rings

JP Tignol, AR Wadsworth - 2015 - Springer
The theory of finite-dimensional division algebras witnessed several breakthroughs in the
latter decades of the twentieth century. Important advances, such as Amitsur's construction of …

Linear groups

AE Zalesskii - Russian Mathematical Surveys, 1981 - iopscience.iop.org
Abstract CONTENTS Introduction Chapter I. Methods for infinite linear groups § 1. The
method of algebraic groups § 2. The Mal'tsev-Platonov approximation method § 3 …

The Tannaka-Artin problem and reduced K-theory

VP Platonov - Mathematics of the USSR-Izvestiya, 1976 - iopscience.iop.org
We solve the old Tannaka-Artin problem, which states the following in modern terminology:
is the reduced Whitehead group SK 1 (A) of a finite-dimensional division algebra A trivial …

Проблема Таннака–Артина и приведенная К-теория

ВП Платонов - Изв. АН СССР, сер. мат, 1976 - mathnet.ru
ВППлатонов, “Проблема Таннака–Артина и приведенная $K$-теория”, Изв. АН СССР. Сер.
матем., 40:2 (1976), 227–261; Math. USSR-Izv., 10:2 (1976), 211–243 Известия Академии …

Finite-dimensional division algebras

VP Platonov, VI Yanchevskii - Algebra IX: Finite Groups of Lie Type Finite …, 1996 - Springer
The beginning of investigations into finite-dimensional division algebras was made by Sir
William Hamilton in 1843, when he discovered the algebra of real quaternions, which rapidly …

Гензелевы алгебры с делением и приведенные унитарные группы Уайтхеда для внешних форм анизотропных алгебраических групп типа

ВИ Янчевский - Математический сборник, 2022 - mathnet.ru
Получены результаты о строении инволютивных гензелевых слабо разветвленных
алгебр с делением, которые затем используются при получении формул для …

Reduced Whitehead groups and the conjugacy problem for special unitary groups of anisotropic Hermitian forms

VI Yanchevskii - Journal of Mathematical Sciences, 2013 - Springer
Let K/k be a separable field extension of degree 2, D be a finite-dimensional central division
algebra over K with a K/k-involution τ, h be an Hermitian anisotropic form on a right D-vector …

Whitehead groups of spinor groups

AP Monastyrnyĭ, VI Yanchevskiĭ - Mathematics of the USSR …, 1991 - iopscience.iop.org
The Whitehead groups of spinor groups are studied. The known Kneser-Tits conjecture for
spinor groups is reduced to a spinor analogue of the Tannaka-Artin problem, namely, to the …

Reduced unitary K-theory and division rings over discretely valued Hensel fields

VI Jančevskiĭ - Mathematics of the USSR-Izvestiya, 1979 - iopscience.iop.org
In this paper a Hermitian analog of reduced K-theory is constructed. The author studies the
reduced unitary Whitehead groups SUK 1 (A) of simple finite-dimensional central algebras A …

On the triviality of certain Whitehead groups

N Grenier-Boley - Mathematical Proceedings of the Royal Irish Academy, 2007 - JSTOR
Let K be a field of arbitrary characteristic and let q be a prime number different from the
characteristic of K. If A is a central simple algebra over whose index is a power of q, we show …