Derivations, isomorphisms, and second cohomology of generalized Witt algebras
Authors:
Dragomir Z. DJ Okovic and Kaming Zhao
Journal:
Trans. Amer. Math. Soc. 350 (1998), 643664
MSC (1991):
Primary 17B40, 17B65; Secondary 17B56, 17B68
MathSciNet review:
1390977
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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 , 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.
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Additional Information
Dragomir Z. DJ Okovic
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Email:
dragomir@herod.uwaterloo.ca
Kaming Zhao
Affiliation:
Institute of Systems Science, Academia Sinica, Beijing, 100080, China
Address at time of publication:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 537061388
Email:
zhao@math.wisc.edu
DOI:
http://dx.doi.org/10.1090/S0002994798017863
PII:
S 00029947(98)017863
Keywords:
Simple Lie algebras,
derivations,
2cocycles,
automorphism group
Received by editor(s):
January 2, 1996
Received by editor(s) in revised form:
April 8, 1996
Additional Notes:
The first author was supported in part by the NSERC Grant A5285.\endgraf The second author was supported by Academia Sinica of P.R. China.
Article copyright:
© Copyright 1998
American Mathematical Society
