How to "find" this Lie algebra: proof that $\mathfrak{sl}$ is trace zero matrices
117737
Why is $\mathfrak{sl}(n)$ the algebra of traceless matrices?
116159
Derivations on semisimple Lie algebra
70533
In what sense can the Lie algebra of $GL_n(\mathbb{C})$ be "identified" with $M_n(\mathbb C)$?
115414
Lie Algebra of $SL_n(\mathbb H)$
121987
Direct proof that nilpotent matrix has zero trace
82637
Does there exist a non-trivial, associative Lie algebra?
146690
Basis for adjoint representation of $sl(2,F)$
90506
Finite multiplicative group of matrices with sum of traces equal to zero.
72932
Center of Lie group and Lie algebra
39657
Strictly Upper Triangular $n\times n$ Matrices form a Nilpotent Lie Algebra over $\mathbb{C}$ for $n\geq 2$
27056
$ gl(2,\mathbb C) \cong sl(2,\mathbb C) \oplus \mathbb C $
149772
How can a Lie subgroup of a matrix Lie group not be a matrix Lie group
58653
The opposite of Weyl's theorem on Lie algebras
153426
Is the radical of a Lie algebra preserved by all of its derivations?
26958
Classification of 3-dimensional Lie Algebra
55828
What are the generators for $SL_n(\mathbb{R})$ (Michael Artin's Algebra book)
30794
Commutator Group of $GL_2(R)$ is $SL_2(R)$