Gleason parts and point derivations for uniform algebras with dense invertible group II

TL;DR

This paper revisits earlier results on uniform algebras with dense invertible groups, correcting previous proof errors and strengthening some findings, confirming the validity of most original conclusions.

Contribution

It corrects and strengthens previous results on Gleason parts and point derivations in uniform algebras with dense invertible groups.

Findings

Most original results remain valid despite earlier proof errors

Strengthened some of the original theorems

Confirmed the correctness of the main conclusions

Abstract

Due to the omission of a hypothesis from an elementary lemma in the author's paper "Gleason parts and point derivations for uniform algebras with dense invertible group", some of the proofs presented in that paper are flawed. We prove here that nevertheless, all of the results in that paper, with the exception of the one misstated lemma, are correct. In the process, we strengthen slightly some of the results of that paper.