Why the Lie algebra of $\mathrm{SL}(2, \mathbb{C})$ are traceless matrices?
51889
How to "find" this Lie algebra: proof that $\mathfrak{sl}$ is trace zero matrices
8456
Prove that $SL(2,\mathbb{R})$ acts transitively on the upper half plane
60663
Let $\rho$ f.d. rep of a nilpotent Lie algebra such that $\rm{det} \rho(X) = 0$, $\forall X$. Then $\exists v \neq 0$: $\rho(X)v = 0, \forall X$.
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
69694
Classify orbits of conjugating action on $GL_2(\mathbb{C})$
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
68014
Prove that $\mathfrak{su}(2)$ is not isomorphic to $\mathfrak{sl}(2,\mathbb R)$
62219
Under what conditions is the exponential map on a Lie algebra injective?
114626
Lie Algebra of U(N) and SO(N)
153426
Is the radical of a Lie algebra preserved by all of its derivations?
60005
Determining the Orbits/Orbit Space of $O(3)$ on Real 3 by 3 Traceless Symmetric Matrices
124245
How are groups with the same Lie Algebra inequivalent?
84677
An Explicit Isomorphism Between the Three Dimensional Orthogonal Lie Algebra and the Special Linear Lie Algebra of Dimension $3$
13292
Which of $\{J_0,J_1,J_2\}$ and $\{J_0,J_+,J_-\}$ is a generator for the Lie algebra $\mathfrak{su}(2)$?
121987
Direct proof that nilpotent matrix has zero trace
86224
The root system of $sl(3,\mathbb C)$
27056
$ gl(2,\mathbb C) \cong sl(2,\mathbb C) \oplus \mathbb C $