On the simplicity of some kac-moody groups

Abstract

Recently, Marcuson extended the classical construction of Tits systems in Steinberg groups to include the Kac-Moody Steinberg groups associated with the infinite dimensional versions of the great Lie algebras. If these Lie algebras and their Kac-Moody groups are viewed as limits of their finite dimensional counterparts, more direct methods may be employed. In fact, the Kac-Moody Chevalley groups of these Lie algebras are seen to be simple.

Keywords:

• Chevalley groups
• Lie algebras
• Steinberg groups
• Tits systems
• 1991 Mathematics Subject Classifications: Primary: 17B65; Secondary: 20E42

^∗Present Address: Mathematics, 4902 Valley East Boulevard No.F, Areata, California 95521

^∗Present Address: Mathematics, 4902 Valley East Boulevard No.F, Areata, California 95521

Notes

^∗Present Address: Mathematics, 4902 Valley East Boulevard No.F, Areata, California 95521