Nilpotent Lie Algebra with determinant 0
60663
Let $\rho$ f.d. rep of a nilpotent Lie algebra such that $\rm{det} \rho(X) = 0$, $\forall X$. Then $\exists v \neq 0$: $\rho(X)v = 0, \forall X$.
112690
Lie Group Decomposition as Semidirect Product of Connected and Discrete Groups
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
61868
Prove that $ND = DN$ where $D$ is a diagonalizable and $N$ is a nilpotent matrix.
125980
Isomorphic Lie Algebra $so(4)$ and $su(2) \times su(2)$
34294
Two Definitions of the Special Orthogonal Lie Algebra
87922
Computing the Lie bracket on the Lie group $GL(n, \mathbb{R})$
123595
Representations of Direct Sum of Lie Algebras
114569
How do you find the Lie algebra of a Lie group (in practice)?
96770
Explicit isomorphism between the four dimensional orthogonal Lie algebra and the direct sum of special linear Lie algebras of dimension 3.
34445
Why is the determinant of a symplectic matrix 1?
130268
How to prove that a nilpotent matrix is not invertible?
114626
Lie Algebra of U(N) and SO(N)
22563
Units and Nilpotents
144531
How to prove that a nilpotent operator has a basis representation that is strictly upper triangular?
50404
How to prove a matrix is nilpotent?
20479
Radical of a Lie algebra bracket itself