Nilpotent Lie algebras of Kac–Moody affine type

Realization of locally extended affine Lie algebras of type $A_1$

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

Affine structures on nilpotent contact Lie algebras

Any Lie algebra equipped with a symplectic form can be equipped with an affine structure. On the other hand there exist (2p + 1)-dimensional Lie algebras with contact form and no affine structure. But each nilpotent contact Lie algebra is a one-dimensional central extension of a symplectic algebra. The aim of this work is to study how we can extend, under certain conditions, the symplectic stuc...

Some properties of nilpotent Lie algebras

In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.

Lie Algebras of Finite and Affine Type

realization of locally extended affine lie algebras of type $a_1$

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...