Hopf algebra
A Hopf algebra is a bialgebra
A over a field 𝕂 with a 𝕂-linear map S:A→A,
called the antipode, such that
m∘(S⊗id)∘Δ=η∘ε=m∘(id⊗S)∘Δ, | (1) |
where m:A⊗A→A is the multiplication map m(a⊗b)=ab and η:𝕂→A is the unit map η(k)=k1I.
In of a commutative diagram: