ON THE NILPOTENCY OF CERTAIN SUBALGEBRAS OF KAC-MOODY ALGEBRAS OF TYPE AN(r)

Title & Authors
ON THE NILPOTENCY OF CERTAIN SUBALGEBRAS OF KAC-MOODY ALGEBRAS OF TYPE AN(r)
Kim, Yeon-Ok; Min, Seung-Kenu;

Abstract
Let (equation omitted) be a symmetrizable Kac-Moody algebra with the indecomposable generalized Cartan matrix A and W be its Weyl group. Let $\small{\theta}$ be the highest root of the corresponding finite dimensional simple Lie algebra $\small{{\gg}}$ of g. For the type $\small{{A_N}^{(r)}}$, we give an element $\small{\omega_{o}\;\in\;W}$ such that $\small{{{\omega}_o}^{-1}({\{\Delta\Delta}_{+}})\;=\;{\{\Delta\Delta}_{-}}}$. And then we prove that the degree of nilpotency of the subalgebra (equation omitted) is greater than or equal to $\small{ht{\theta}+1}$.
Keywords
affine Lie algebra;Weyl group;root system;degree of nilpotency;
Language
English
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