Derivations, isomorphisms, and second cohomology of generalized Witt algebras
Derivations, isomorphisms, and second cohomology of generalized Witt algebras
复制标题
DOI：
10.1090/s0002-9947-98-01786-3
复制
发表时间：
1998
影响因子：
1.3
通讯作者：
Dragomir Ž. Đ Oković;Kaming Zhao
中科院分区：
文献类型：
--
作者：
Dragomir Ž. Đ Oković;Kaming Zhao
特征为0的域F上的广义Witt代数是由Kawamoto在12年前定义的。本文利用与Kawamoto不同的符号，给出了F上广义Witt代数W = W（A，T，φ）的一个本质等价的定义，这里的成分是交换群A，F上的向量空间T和映射φ：T × A → K，它在第一个变量上是线性的，在第二个变量上是可加的.本文给出了任意广义Witt代数W = W（A，T，φ）的导子的显式刻画，并完全确定了任意两个单广义Witt代数之间的同构，计算了任意单广义Witt代数的第二上同调群H2（W，F）.一些特殊的广义Witt代数的导子、自同构和二阶上同调群已经被其他几位作者研究过，如文献中所指出的。
Generalized Witt algebras, over a field F of characteristic 0, were defined by Kawamoto about 12 years ago. Using different notations from Kawamoto’s, we give an essentially equivalent definition of generalized Witt algebras W = W (A,T, φ) over F , where the ingredients are an abelian group A, a vector space T over F , and a map φ : T × A → K which is linear in the first variable and additive in the second one. In this paper, the derivations of any generalized Witt algebra W = W (A, T, φ), with the right kernel of φ being 0, are explicitly described; the isomorphisms between any two simple generalized Witt algebras are completely determined; and the second cohomology group H2(W,F ) for any simple generalized Witt algebra is computed. The derivations, the automorphisms and the second cohomology groups of some special generalized Witt algebras have been studied by several other authors as indicated in the references.