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浙江大学学报（理学版）
浙江大学学报（理学版）  2021, Vol. 48 Issue (2): 174-179    DOI: 10.3785/j.issn.1008-9497.2021.02.006
数学与计算机科学     
素特征域上Witt代数及极大子代数的2-局部导子
姚裕丰, 王惠
上海海事大学 文理学院，上海 201306
2-local derivations of the Witt algebra and its maximal subalgebra over a field of prime characteristic
YAO Yufeng, WANG Hui
College of Arts and Sciences , Shanghai Maritime University, Shanghai 201306, China
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摘要： 李代数的导子代数对李代数结构的研究有重要作用。特征零的代数闭域上有限维半单李代数的导子都是内导子，该类李代数同构于其导子代数。作为导子的自然推广，李代数的2-局部导子对李代数局部性质的研究，具有重要作用，研究了素特征域上李代数的2-局部导子。设F是特征p>3的代数闭域，g是域F上p-维Witt代数，g0是g的极大子代数，讨论了g和g0的2-局部导子的性质，证明了g和g0的所有2-局部导子均为导子。
关键词： 2-局部导子;  Witt代数;  导子    
Abstract: The derivation algebra of a Lie algebra plays an important role to study of the structure of the Lie algebra. All derivations of finite dimensional semisimple Lie algebras over an algebraically closed field are inner. So the Lie algebras of this kind are isomorphic to their derivation algebras. As a natural generalization of derivation,2-local derivation of a Lie algebra plays an important role in study of local properties of the Lie algebra.This paper is devoted to study 2-local derivations of Lie algebras over fields of prime characteristic.Let g be the p dimensional Witt algebra over an algebraically closed field of characteristic p>3,g0 be its maximal subalgebra. We investigate the properties of 2-local derivations on g and g0,and show that all 2-local derivations on g and g0 are derivations.
Key words: 2-local derivation    Witt algebra    derivation
收稿日期: 2020-01-17 出版日期: 2021-03-18
CLC:  O  
基金资助: 国家自然科学基金资助项目(11771279,12071136).
作者简介: 姚裕丰(1982—),ORCID:http:orcid.org/0000-0002-9469-2030，男，博士，教授，主要从事李理论及表示理论研究，E-mail:yfyao@shmtu.edu.c；
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引用本文:

姚裕丰, 王惠. 素特征域上Witt代数及极大子代数的2-局部导子[J]. 浙江大学学报（理学版）, 2021, 48(2): 174-179.

YAO Yufeng, WANG Hui. 2-local derivations of the Witt algebra and its maximal subalgebra over a field of prime characteristic. Journal of Zhejiang University (Science Edition), 2021, 48(2): 174-179.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2021.02.006    或    https://www.zjujournals.com/sci/CN/Y2021/V48/I2/174

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