Hopf theory MOC

Sweedler’s large Hopf algebra

Sweedler’s large Hopf algebra 𝐻 is an infinite-dimensional commutative noncocommutative Hopf algebra generated as a 𝕂-monoid by {𝑥,𝑔,𝑔−1}, hopf with comultiplication

Δ𝑔=𝑔⊗𝑔,Δ𝑥=1⊗𝑥+𝑥⊗𝑔;

coünit

𝜖(𝑥)=0,𝜖(𝑔)=1;

and thus antipous

𝑆(𝑥)=−𝑥𝑔−1,𝑆(𝑔)=𝑔−1.

A quotient is Sweedler’s small Hopf algebra 𝐻4.

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