Killing form on some Lie algebra $L$ is zero. Is $L$ necessarily nilpotent?
24249
When is the Killing form null?
35509
Noether's Theorem: Lie groups vs. Lie algebras; finite vs. infinitesimal symmetries
33423
Decomposition of semisimple Lie algebra via its roots
39334
Non-degenerate bilinear forms and invertible matrices
115273
Nilpotent matrix and basis for $F^n$
96770
Explicit isomorphism between the four dimensional orthogonal Lie algebra and the direct sum of special linear Lie algebras of dimension 3.
13371
Show that the Lie algebra generated by x, y with relations $ad(x)^2(y) = ad(y)^5(x) = 0$ is infinite dimensional and construct a basis
28460
Show matrix is nilpotent
72932
Center of Lie group and Lie algebra
118396
Non abelian Lie group with abelian Lie algebra
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
78298
On the nilpotence of the matrix $AB-BA$
101229
Lie algebra of $\left(\begin{smallmatrix}a & b\\ & a^2\end{smallmatrix}\right )$ in $GL_2(\mathbb{R})$
23535
Describing the Lie algebra structure of a semi-direct product of Lie groups
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
39657
Strictly Upper Triangular $n\times n$ Matrices form a Nilpotent Lie Algebra over $\mathbb{C}$ for $n\geq 2$
10001
Prove that the only eigenvalue of a nilpotent operator is 0?