A Lie algebra is nilpotent if acting on any one of its elements with other elements, via the Lie bracket, repeatedly eventually yields zero.
The lower central series or descending central series? of a Lie algebra is a sequence of nested ideals defined inductively by , . The Lie algebra is said to be nilpotent if for some .
In other words, a Lie algebra is nilpotent if and only the improper ideal is a nilpotent element in the ideal lattice with respect to the ideal product .
A finite-dimensional Lie algebra is nilpotent precisely if its Chevalley-Eilenberg algebra is a Sullivan algebra (necessarily minimal). See also at rational homotopy theory for more on this.
Nilpotent Lie algebras (pdf)
Wikipedia, Nilpotent Lie algebra
Last revised on November 22, 2017 at 05:55:46. See the history of this page for a list of all contributions to it.