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 \${{\omega}_o}^{-1}({\{\Delta\Delta}_{+}})\;
Keywords
affine Lie algebra;Weyl group;root system;degree of nilpotency;
Language
English
Cited by
References
1.
Tohoku Math. J., vol.47. pp.391-403

2.
Introduction to Lie Algebras and Representation Theory,

3.
Infinite-Dimensional Lie Algebras,

4.
Commun. Korean Math. Soc., vol.16. 1, pp.85-94

5.
Tohoku Math. J., vol.40. 4, pp.645-650

6.
Introduction to Kac-Moody Algebra,