Derivations, isomorphisms, and second cohomology of generalized Witt algebras |
| |
Authors: | Dragomir Z DJ Okovic Kaming Zhao |
| |
Institution: | Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada ; Institute of Systems Science, Academia Sinica, Beijing, 100080, China |
| |
Abstract: | Generalized Witt algebras, over a field of characteristic , were defined by Kawamoto about 12 years ago. Using different notations from Kawamoto's, we give an essentially equivalent definition of generalized Witt algebras over , where the ingredients are an abelian group , a vector space over , and a map which is linear in the first variable and additive in the second one. In this paper, the derivations of any generalized Witt algebra ![$W=$](http://www.ams.org/tran/1998-350-02/S0002-9947-98-01786-3/gif-abstract/img12.gif)
, with the right kernel of being , are explicitly described; the isomorphisms between any two simple generalized Witt algebras are completely determined; and the second cohomology group 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. |
| |
Keywords: | Simple Lie algebras derivations 2-cocycles automorphism group |
|
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文 |
|