Automorphisms and Derivations of Certain Solvable Lie Algebras Over Commutative Rings
Automorphisms and Derivations of Certain Solvable Lie Algebras Over Commutative Rings
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交换环上某些可解李代数的自同构及其导数
DOI：
10.1080/00927872.2010.536961
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Zhengxin Chen
中科院分区：
文献类型：
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作者：
Zhengxin Chen
设L是有限维复单李代数，L <$是L的Chevalley基的n-跨距，LR = R <$$> L <$是有单位元的交换环R上的L型Chevalley代数.设R是由极大toral子代数的基元和与正根相关的根向量所张成的LR的可解子代数。本文证明了在一定条件下，R的任意自同构都唯一分解为图自同构、对角自同构和内自同构的乘积，R的任意导子都唯一分解为根向量诱导的内导子与对角导子之和.相应地，确定了R的自同构群和导子代数。
Let L be a finite-dimensional complex simple Lie algebra, L ℤ be the ℤ-span of a Chevalley basis of L, and L R = R ⊗ℤ L ℤ be a Chevalley algebra of type L over a commutative ring R with identity. Let ℬ(R) be the solvable subalgebra of L R spanned by the basis elements of the maximal toral subalgebra and the root vectors associated with positive roots. In this article, we prove that under some conditions for R, any automorphism of ℬ(R) is uniquely decomposed as a product of a graph automorphism, a diagonal automorphism and an inner automorphism, and any derivation of ℬ(R) is uniquely decomposed as a sum of an inner derivation induced by root vectors and a diagonal derivation. Correspondingly, the automorphism group and the derivation algebra of ℬ(R) are determined.
DOI：
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发表时间：
2005
期刊：
影响因子：
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作者：
T. Kobayashi;T. Oshima
通讯作者：
T. Oshima