Lyrics
[Rapping]
[Verse 1]
In the world of math, we break it down to a base,
Abstract algebra, we need to see its face,
Linear transformations, making them concrete,
Matrices and modules where theories meet.
[Rapping]
[Verse 2]
Vectors and fields, the space we need to choose,
Real or complex, n-dimensional views,
Groups, algebras, Lie, we analyze their state,
Invertible matrices, the forms they create.
[Singing]
[Chorus]
Representation theory, make it clear,
Abstract objects, bring them near,
Matrices and vectors, feel the beat,
Concrete algebra, can't be beat.
[Rapping]
[Verse 3]
Mappings and actions, how they interact,
Group or algebra, the way they act,
Homomorphisms, linear and clean,
Group elements to maps, in this scene.
[Singing]
[Chorus]
Representation theory, make it clear,
Abstract objects, bring them near,
Matrices and vectors, feel the beat,
Concrete algebra, can't be beat.
[Rapping]
[Verse 4]
Irreducible reps, subspaces in play,
If stable under action, subrepresentation we say,
Trivial to full, no in-between scene,
It's reducible if there's more to glean.
[Rapping]
[Verse 5]
Schur's lemma tells, in a crisp clear line,
Equivariant maps are scalar, by design,
Zero or isomorphisms, no middle ground,
In a closed field, this truth is found.
[Rapping]
[Verse 6]
Characters and weights, they play their role,
Symmetries and structures, making math whole,
Theorems and lemmas, in reps they shine,
Guiding the way through algebraic design.
[Singing]
[Chorus]
Representation theory, make it clear,
Abstract objects, bring them near,
Matrices and vectors, feel the beat,
Concrete algebra, can't be beat.
[Singing]
[Chorus]
Representation theory, make it clear,
Abstract objects, bring them near,
Matrices and vectors, feel the beat,
Concrete algebra, can't be beat.
