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 n≥2. An invertible linear map ϕ:gl(n,C)→gl(n,C) preserves solvability in both directions if both ϕ and ϕ−1 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.
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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