
Journal of Lie Theory 14 (2004), No. 1, 011023 Copyright Heldermann Verlag 2004 On the Nilpotency of Certain Subalgebras of KacMoody Lie Algebras Yeonok Kim Dept. of Mathematics, Soong Sil University, Seoul 151, South Korea, yokim@ssu.ac.kr Kailash C. Misra, Ernie Stitzinger Dept. of Mathematics, North Carolina State University, Raleigh, NC 276958205, USA, misra@math.ncsu.edu, stitz@math.ncsu.edu [Abstractpdf] Let $\g = \n_\oplus\h\oplus\n_+$ be an indecomposable KacMoody Lie algebra associated with the generalized Cartan matrix $A=(a_{ij})$ and $W$ be its Weyl group. For $w \in W$, we study the nilpotency index of the subalgebra $S_w =\n_+ \cap w(\n_)$ and find that it is bounded by a constant $k=k(A)$ which depends only on $A$ but not on $w$ for all $A=(a_{ij})$ finite, affine of type other than $E$ or $F$ and indefinite type with $a_{ij} \geq 2$. In each case we find the best possible bound $k$. In the case when $A=(a_{ij})$ is hyperbolic of rank two we show that the nilpotency index is either 1 or 2. [ Fulltextpdf (197 KB)] for subscribers only. 