Loading [MathJax]/jax/output/CommonHTML/jax.js
Journals
Resources
About Us
Open Access
Go to previous page

Invertible Linear Maps on the General Linear Lie Algebras Preserving Solvability

Invertible Linear Maps on the General Linear Lie Algebras Preserving Solvability

Year:    2012

Author:    Zhengxin Chen, Qiong Chen

Communications in Mathematical Research , Vol. 28 (2012), Iss. 1 : pp. 26–42

Abstract

Let Mn be the algebra of all n×n complex matrices and gl(n,C) be the general linear Lie algebra, where n2. An invertible linear map ϕ:gl(n,C)gl(n,C) preserves solvability in both directions if both ϕ and ϕ1 map every solvable Lie subalgebra of gl(n,C) to some solvable Lie subalgebra. In this paper we classify the invertible linear maps preserving solvability on gl(n,C) in both directions. As a sequence, such maps coincide with the invertible linear maps preserving commutativity on Mn in both directions.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2012-CMR-19067

Communications in Mathematical Research , Vol. 28 (2012), Iss. 1 : pp. 26–42

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    general linear Lie algebra solvability automorphism of Lie algebra.

Author Details

Zhengxin Chen Email

Qiong Chen Email