2-Local derivations on generalized Witt algebras
2-Local derivations on generalized Witt algebras
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DOI：
10.1080/03081087.2019.1708846
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发表时间：
2019-12
影响因子：
1.1
通讯作者：
Sh. A. Ayupov;K. Kudaybergenov;B. Yusupov
中科院分区：
文献类型：
--
作者：
Sh. A. Ayupov;K. Kudaybergenov;B. Yusupov
本文研究了无限维广义Witt代数上的2-局部导子。首先证明了向量空间上广义Witt代数的2-局部导子是导子，其中是特征为零的域。进一步我们考虑了域上的广义Witt代数，其中I是一个无限指标集，并且证明了域上的所有2-局部导子也是导子。最后，证明了的Borel子代数上的2-局部导子是导子.
In the present paper, we study 2-local derivations on the so-called infinite dimensional generalized Witt algebras. Firstly, we prove that every 2-local derivation on the generalized Witt algebra over the vector space is a derivation, where is a field of characteristic zero. Further we consider generalized Witt algebras of the form over the field , where I is an infinite index set and and prove that all 2-local derivations on are also derivations. Finally, we show that every 2-local derivation on the Borel subalgebra of is a derivation.