Matrix lie rings that contain an abelian subring

Evgenii L. Bashkirov
Department of Physics and Mathematics, Smolensk State University, Przhevalsky st. 4, Smolensk 214000 Russia.

\(^{1}\)Corresponding Author: bashkirov57@mail.ru

Copyright © 2008 Evgenii L. Bashkirov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2008.

Abstract

Let \(k\) be a field and \(\overline{k}\) an algebraic closure of \(k\). The paper is devoted to the description of subrings of the Lie ring \(sl_{2}overline{k}\) that contain an abelian subring which is a one-dimensional subspace of the \(k\)-vector space \(sl_{2}overline{k}\).

Keywords:

Lie rings, lie algebras, semi-simple matrices, nilpotent matrices.