TITLE:
On the Initial Subalgebra of a Graded Lie Algebra
AUTHORS:
Thomas B. Gregory
KEYWORDS:
Prime-Characteristic Lie Algebras
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.9,
September
22,
2014
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.