$(\mathbb{R}^{3},\times)$ is a Lie algebra that does not have Lie subalgebras of dimension 2.
89805
2-dimensional Lie subgroups of $SO(3)$
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
76048
Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$?
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
137761
Why are the fundamental and anti-fundamental representation in $\text{SL}(2,\mathbb{C})$ not equivalent?
84677
An Explicit Isomorphism Between the Three Dimensional Orthogonal Lie Algebra and the Special Linear Lie Algebra of Dimension $3$
132653
How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
95686
$Lie(G \times H)\cong Lie(G)\oplus Lie(H)$
70533
In what sense can the Lie algebra of $GL_n(\mathbb{C})$ be "identified" with $M_n(\mathbb C)$?
34294
Two Definitions of the Special Orthogonal Lie Algebra
147148
why is $S^2$ not a Lie group?
69611
If $R$ and $S$ are rings then $R \times S$ is never a field
126295
What is an $R$-algebra?
86667
Is the 1-Dimensional Lie algebra Simple?
18893
$\varphi:G\to H$ is a Lie Group Homomorphism, then $\ker \varphi$ has Lie algebra $\ker D_e \varphi$
77112
Artinian rings that are not Artin algebras
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$