∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
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.
Victor Kac (notes by Marc Doss), Nilpotent and Solvable Lie algebras (2010) [pdf, pdf]
Nilpotent Lie algebras (pdf)
Wikipedia, Nilpotent Lie algebra
On the Sullivan models which are Chevalley-Eilenberg algebra of nilpotent Lie algebras:
Last revised on November 30, 2023 at 12:13:59. See the history of this page for a list of all contributions to it.