Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 14, No. 1, pp. 11--23 (2004)

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On the nilpotency of certain subalgebras of Kac-Moody Lie algebras

Yeonok Kim, Kailash C. Misra, and Ernie Stitzinger

Yeonok Kim
Department of Mathematics
Soong Sil University
Seoul 151
Kailash C. Misra and
Ernie Stitzinger
Department of Mathematics
North Carolina State University
Raleigh, NC 27695-8205

Abstract: Let $\g = \n_-\oplus\h\oplus\n_+$ be an indecomposable Kac-Moody 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.

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Electronic version published on: 29 Jan 2004. This page was last modified: 1 Sep 2004.

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