New posts in Lie Algebras

Show that if $\Omega_1,\Omega_2$ are tangent vectors of curves in $SO(3)$ then $[\Omega_1,\Omega_2]\in\mathfrak{so}(3)$

Showing the Lie Algebras $\mathfrak{su}(2)$ and $\mathfrak{sl}(2,\mathbb{R})$ are not isomorphic.

If $\mathfrak{g}=\bigoplus\mathfrak{g}_i$ is a semisimple Lie algebra, why does $\mathfrak{h}=\bigoplus\left(\mathfrak{h}\cap\mathfrak{g}_i\right)$?

Solvable equivalent to nilpotency of first derived Lie algebra?

Is there an infinite dimensional Lie group associated to the Lie algebra of all vector fields on a manifold?

Linear homomorphisms of square matrices are conjugations

Normal Subgroups of $SU(n)$

Are there common inequivalent definitions of Cartan subalgebra of a real Lie algebra?

Examples of Free Lie Algebra

Campbell-Baker-Hausdorff formula for $\log(\exp(X+Y)\exp(X-Y))$