Talk:Sweedler's Hopf algebra

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About the introduction : 'In mathematics, Moss E. Sweedler (1969, p. 89–90) introduced an example of an infinite-dimensional Hopf algebra, and Sweedler's Hopf algebra H4 is a certain 4-dimensional quotient of it that is neither commutative nor cocommutative.'

In order to construct his Hopf algebra H_4, Sweedler defines a bialgebra F (that is infinite dimensional as a vector space) but I don't think that this bialgebra is a Hopf algebra. What is the antipode of F?