Inner automorphisms of shift-invariant algebras on compact groups. (Q5942592)

Let \(G\) be a compact connected abelian group. The \(G\)-invariant uniform subalgebras of the space \(C(G)\) of continuous functions on \(G\) are spaces of functions whose Fourier transform is supported by a semi-subgroup \(S\) of the dual group of \(G\). When \(S\) defines a total order on the dual group, the corresponding algebra \(A_S\) is a so-called ``big disc algebra''. Extending classical work of Arens and Singer, the authors show that if \(A_S\) is a subalgebra of a big disc algebra and if there is no nontrivial idempotent homomorphism on \(S\), then either \(S\) is the subgroup of nonnegative integers or every automorphism of \(A_S\) is inner.