An easy proof for the uniqueness of integrals (Q2762044)

As advertised in the title, this paper gives a proof of Sullivan's result from the early 1970's that the space of left integrals for a Hopf algebra \(H\) over a field \(k\) has dimension at most 1. The proof requires the fact that \(H\) has a nonzero left integral iff the injective hull \(J\) of \(k1\) is finite-dimensional. The remainder of the proof is an exercise requiring agility with the summation notation and repeated use of the definition of left and right integral.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00024].