Journal of Lie Theory Vol. 14, No. 1, pp. 1123 (2004) 

On the nilpotency of certain subalgebras of KacMoody Lie algebrasYeonok Kim, Kailash C. Misra, and Ernie StitzingerYeonok KimDepartment of Mathematics Soong Sil University Seoul 151 Korea yokim@ssu.ac.kr and Kailash C. Misra and Ernie Stitzinger Department of Mathematics North Carolina State University Raleigh, NC 276958205 USA misra@math.ncsu.edu stitz@math.ncsu.edu Abstract: 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. Full text of the article:
Electronic version published on: 29 Jan 2004. This page was last modified: 1 Sep 2004.
© 2004 Heldermann Verlag
