APM  Vol.4 No.9 , September 2014
On the Initial Subalgebra of a Graded Lie Algebra
Author(s) Thomas B. Gregory*
ABSTRACT
We show that each irreducible, transitive finite-dimensional graded Lie algebra over a field of prime characteristic p contains an initial subalgebra in which the pth power of the adjoint transformation associated with any element in the lowest gradation space is zero.

Cite this paper
Gregory, T. (2014) On the Initial Subalgebra of a Graded Lie Algebra. Advances in Pure Mathematics, 4, 513-517. doi: 10.4236/apm.2014.49058.
References
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http://dx.doi.org/10.1080/00927879608825563

[5]   Benkart, G.M., Gregory, T.B. and Kuznetsov, M.I. (1998) On Graded Lie Algebras of Characteristic Three with Classical Reductive Null Component. In: Ferrar, J.C. and Harada, K., Eds., The Monsteer and Lie Algebras, Vol. 7, Ohio State University Mathematical Research Publications, 149-164.

[6]   Gregory, T.B. and Kuznetsov, M.I. (2004) On Depth-Three Graded Lie Algebras of Characteristic Three with Classical Reductive Null Component. Communications in Algebra, 32, 3339-3371.
http://dx.doi.org/10.1081/AGB-120039401

[7]   Gregory, T.B. and Kuznetsov, M.I. On Graded Lie Algebras of Characteristic Three with Classical Reductive Null Component. (In Preparation)

[8]   Weisfeiler, B.J. (1978) On the Structure of the Minimal Ideal of Some Graded Lie Algebras in Characteristic p > 0. Journal of Algebra, 53, 344-361. http://dx.doi.org/10.1016/0021-8693(78)90280-6

[9]   Benkart, G.M. and Gregory, T.B. (1989) Graded Lie Algebras with Classical Reductive Null Component. Mathematische Annalen, 285, 85-98. http://wdx.doi.org/10.1007/BF01442673

[10]   Jacobson, N. (1962) Lie Algebras, Tracts in Mathematics. Vol. 10, Interscience, New York.

 
 
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