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 {π‘₯,𝑔,π‘”βˆ’1}, #m/def/hopf with comultiplication

Δ𝑔=π‘”βŠ—π‘”,Ξ”π‘₯=1βŠ—π‘₯+π‘₯βŠ—π‘”;

coΓΌnit

πœ–(π‘₯)=0,πœ–(𝑔)=1;

and thus antipous

𝑆(π‘₯)=βˆ’π‘₯π‘”βˆ’1,𝑆(𝑔)=π‘”βˆ’1.

A quotient is Sweedler's small Hopf algebra 𝐻4.

#state/tidy | #lang/en | #SemBr