Journal of Lie Theory 21 (2011), No. 2, 457--468
Copyright Heldermann Verlag 2011
Automorphism Groups of Some Stable Lie Algebras
Jongwoo Lee
Graduate School of Railroad, National University of Technology, 172 Kongneung-dong Nowongu, Seoul, Korea
saganlee@snut.ac.kr
Xueqing Chen
Dept. of Mathematics and Computer Sciences, Univ. of Wisconsin, Whitewater, WI 53190, U.S.A.
chenx@uww.edu
Seul Hee Choi
Dept. of Mathematics, University of Jeonju, Jeonju 560-759, Korea
chois@jj.ac.kr
Ki-Bong Nam
Dept. of Mathematics and Computer Sciences, Univ. of Wisconsin, Whitewater, WI 53190, U.S.A.
namk@uww.edu
A degree stable Lie algebra is defined in the paper of K-Bong Nam, and Seul Hee Choi [Degree Stable Lie Algebras I, Algebra Colloquium 13 (2006) 487--494]. The automorphism group AutLie(S+(2)) of the Lie algebra S+(2) and the automorphism group of the Lie algebra W(1,0,2) are also found in this paper. We find the algebra automorphism groups of the Lie algebras W(12,1,1) and W(12,2,0) in this work. We show that the Cartan subalgebras of W(12,1,1) and W(12,2,0) are one dimensional.
Keywords: Simple, Witt algebra, degreeing Lie algebra, Cartan subalgebra.
MSC: 17A36
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