[Verse 1]
When matrices dance, they rarely commute
X times Y minus Y times X gives fruit
The bracket notation shows their fight
Commutators reveal what's left and right
[Chorus]
Five equations, algebra's crown
Commutators spinning round
Jacobi's identity holds the key
Killing forms set structures free
Dynkin diagrams map the way
Simple algebras on display
[Verse 2]
Jacobi's identity, three terms in a chain
Bracket X with Y and Z, then rearrange the game
Cyclic permutations sum to zero clean
The deepest structure that you've ever seen
[Chorus]
Five equations, algebra's crown
Commutators spinning round
Jacobi's identity holds the key
Killing forms set structures free
Dynkin diagrams map the way
Simple algebras on display
[Verse 3]
Killing form takes adjoint maps as friends
Trace of their composition never ends
Kappa measures how the algebra bends
Non-degenerate means semisimple tends
[Bridge]
Cartan's criterion draws the line
Semisimple if the form's divine
When kappa's kernel disappears
The structure's beauty crystal clear
[Verse 4]
Dynkin diagrams, dots and lines so neat
Each simple algebra finds its beat
Classification's masterpiece complete
Root systems make the picture sweet
[Chorus]
Five equations, algebra's crown
Commutators spinning round
Jacobi's identity holds the key
Killing forms set structures free
Dynkin diagrams map the way
Simple algebras on display
[Outro]
From brackets basic to the whole
These five equations tell the soul
Of Lie algebras, pure and true
The deepest math that waits for you