NILPOTENT LIE ALGEBRAS OF MAXIMAL RANK AND OF KAC-MOODY TYPE: F₄⁽¹⁾

Abstract

Let be the Kac-Moody algebra associated to the affine Cartan matrix F ₄ ⁽¹⁾. Each nilpotent Lie algebra of type F ₄ ⁽¹⁾ is isomorphic to a quotient of the positive part of . We determine the isomorphism classes of nilpotent Lie algebras of type F ₄ ⁽¹⁾.

Keywords:

• Nilpotent
• Maximal rank
• Kac-Moody Lie algebras

ACKNOWLEDGMENTS

The authors gratefully acknowledge the help given by Prof. L. Santharoubane in this work.