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Journal of Lie Theory 15 (2005), No. 1, 249--260
Copyright Heldermann Verlag 2005

Nilpotent Lie Algebras of Maximal Rank and of Kac-Moody Type D4(3)

D. Fernández-Ternero
Dep. Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain


Let $\frak g$ be the Kac-Moody algebra associated with the twisted affine Cartan matrix $D_4^{(3)}$. Each nilpotent Lie algebra of maximal rank and of type $D_4^{(3)}$ is isomorphic to a quotient of the positive part of $\frak g$. We determine the isomorphism classes of nilpotent Lie algebras of maximal rank and of type $D_4^{(3)}$.

Keywords: Nilpotent, maximal rank, Kac-Moody algebras.

MSC: 17B30; 17B67

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