Abstract
LetLbe a finite dimensional simple Lie algebra of absolute toral rank 2 over an algebraically closed field of characteristicp>3 andTa 2-dimensional torus in the semisimplep-envelope ofL. Suppose thatLis not isomorphic to a Melikian algebra. It is proved in this paper that, for every root α∈Γ(L,T), the subalgebraK′(α) generated by ∑i∈F*pKiα(whereKiα={x∈Liα∣α([x,L−iα])=0}) acts triangulably onL. In particular, this implies that, in the terminology of R. E. Block and R. L. Wilson (1988,J. Algebra114, 115–259), all roots of Γ(L,T) are nonexceptional.
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