Invertible linear maps on Borel subalgebras preserving zero Lie products

JOURNAL OF ALGEBRA

卷:406

Article

Wang, Dengyin

关键词: Simple Lie algebras;    Borel subalgebras;    Automorphisms of Lie algebras;   

DOI  :  10.1016/j.jalgebra.2014.02.023

来源: Elsevier

【 摘 要 】

Let g be a simple Lie algebra of rank 1 over an algebraically closed field of characteristic zero, b a Borel subalgebra of g. An invertible linear map phi on b is said preserving zero Lie products in both directions if for x, y is an element of b, [x, y] = 0 if and only if [phi(x), phi(y)] = 0. In this paper, it is shown that an invertible linear map phi on b preserving zero Lie products in both directions if and only if it is a composition of an inner automorphism, a graph automorphism, a scalar multiplication map and a diagonal automorphism, which extends the main result in [8] from a linear solvable Lie algebra to far more general cases. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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