The classification of two step nilpotent complex Lie algebras of dimension $8$

@article{Yan2013,
abstract = {A Lie algebra $\mathfrak \{g\}$ is called two step nilpotent if $\mathfrak \{g\}$ is not abelian and $[\mathfrak \{g\},\mathfrak \{g\}]$ lies in the center of $\mathfrak \{g\}$. Two step nilpotent Lie algebras are useful in the study of some geometric problems, such as commutative Riemannian manifolds, weakly symmetric Riemannian manifolds, homogeneous Einstein manifolds, etc. Moreover, the classification of two-step nilpotent Lie algebras has been an important problem in Lie theory. In this paper, we study two step nilpotent indecomposable Lie algebras of dimension $8$ over the field of complex numbers. Based on the study of minimal systems of generators, we choose an appropriate basis and give a complete classification of two step nilpotent Lie algebras of dimension $8$.},
author = {Yan, Zaili, Deng, Shaoqiang},
journal = {Czechoslovak Mathematical Journal},
keywords = {two-step nilpotent Lie algebra; base; minimal system of generators; related sets; $H$-minimal system of generators; classification; two-step nilpotent; Lie algebra of dimension eight},
language = {eng},
number = {3},
pages = {847-863},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The classification of two step nilpotent complex Lie algebras of dimension $8$},
url = {http://eudml.org/doc/260604},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Yan, Zaili
AU - Deng, Shaoqiang
TI - The classification of two step nilpotent complex Lie algebras of dimension $8$
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 847
EP - 863
AB - A Lie algebra $\mathfrak {g}$ is called two step nilpotent if $\mathfrak {g}$ is not abelian and $[\mathfrak {g},\mathfrak {g}]$ lies in the center of $\mathfrak {g}$. Two step nilpotent Lie algebras are useful in the study of some geometric problems, such as commutative Riemannian manifolds, weakly symmetric Riemannian manifolds, homogeneous Einstein manifolds, etc. Moreover, the classification of two-step nilpotent Lie algebras has been an important problem in Lie theory. In this paper, we study two step nilpotent indecomposable Lie algebras of dimension $8$ over the field of complex numbers. Based on the study of minimal systems of generators, we choose an appropriate basis and give a complete classification of two step nilpotent Lie algebras of dimension $8$.
LA - eng
KW - two-step nilpotent Lie algebra; base; minimal system of generators; related sets; $H$-minimal system of generators; classification; two-step nilpotent; Lie algebra of dimension eight
UR - http://eudml.org/doc/260604
ER -