Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE NILPOTENCY OF CERTAIN SUBALGEBRAS OF KAC-MOODY ALGEBRAS OF TYPE AN(r)

  • Published : 2003.07.01
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Abstract

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

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References

  1. Tohoku Math. J. v.47 Root Strings with Two Consecutive Real roots Yuly Billig;Arturo Pianzola https://doi.org/10.2748/tmj/1178225523
  2. Introduction to Lie Algebras and Representation Theory J.E.Humphreys
  3. Infinite-Dimensional Lie Algebras V.G.Kac
  4. Commun. Korean Math. Soc. v.16 no.1 A Note on The Root System of an Affine Lie Algebra of Type $A_2l^ (2)$ Yeonok Kim
  5. Tohoku Math. J. v.40 no.4 Root strings with three or four real roots in Kac-Moody root systems J.Morita https://doi.org/10.2748/tmj/1178227928
  6. Introduction to Kac-Moody Algebra Z.Wan