| 交换环上辛代数和正交代数的抛物子代数的导子 |
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| 引用本文： | 偶世坤,王登银,郑石秋,赖新兴. 交换环上辛代数和正交代数的抛物子代数的导子[J]. 南京大学学报(自然科学版), 2011, 0(1): 60-71 |
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| 作者姓名： | 偶世坤 王登银 郑石秋 赖新兴 |
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| 作者单位： | 江西理工大学理学院;中国矿业大学理学院;河北理工大学理学院; |
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| 基金项目： | 江西省教育厅青年基金项目(GJJ10155) |
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| 摘 要： | 设R是有1的交换环,L是R上的辛代数或正交代数,h是L的极大环面子代数,b是L中包含h的标准Borel子代数.在2∈R可逆的条件下,本文详细描述了b与L之间的中间李代数,并且证明这些中间李代数的导子都是内导子.
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| 关 键 词： | 抛物子代数 李代数的导子 交换环 |
DERIVATIONS OF THE PARABOLIC SUBALGEBRAS OF THE SYMPLECTIC ALGEBRAS AND THE ORTHOGONAL ALGEBRAS OVER A COMMUTATIVE RING |
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| Ou Shikun Wang Dengyin Zheng Shiqiu Lai Xinxing. DERIVATIONS OF THE PARABOLIC SUBALGEBRAS OF THE SYMPLECTIC ALGEBRAS AND THE ORTHOGONAL ALGEBRAS OVER A COMMUTATIVE RING[J]. Journal of Nanjing University: Nat Sci Ed, 2011, 0(1): 60-71 |
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| Authors: | Ou Shikun Wang Dengyin Zheng Shiqiu Lai Xinxing |
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| Affiliation: | Ou Shikun (Faculty of Science,Jiangxi University of Science and Technology,341000,Ganzhou PRC) Wang Dengyin (Department of Mathematics,China University of Mining and Technology,221008,Xuzhou PRC) Zheng Shiqiu (College of Science,Hebei Polytechnic University,063009,Tangshan PRC) Lai Xinxing (Faculty of Science,Ganzhou PRC) |
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| Abstract: | Let R be a commutative ring with identity 1,L the symplectic algebra or the orthogonal algebra over R,h be the maximal torus of L,b the standard Borel subalgebra of L containing h.In this paper,we first determine the intermediate algebras between b and L,then for any given intermediate algebra (?) between b and L,we prove that all its derivations are inner,provided that 2 is invertible in R. |
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| Keywords: | parabolic subalgebras derivations of Lie algebras commutative rings |
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