I’m trying to calculate the order of the antipode in 4(e), and I keep coming up with the same result as in part (c). Conceptually, I don’t see how this can be otherwise, since all we’ve done is impose some relations on the bialgebra. Since modding out preserves equality, then if in , then we should have in . This implies that the order of in should be less than or equal to the order of in . However, problem 4(e) implies that we can make the order of as large as we like in by picking a sufficiently large . Anyone feel like weighing in?
HW #3, 4(e)