On p-standard table algebras of order p3, II

Abstract

The classification is here completed for the p-standard table algebras of order p3 for any rational prime p. These include the adjacency algebras of p-schemes of order p3. The remaining case, where the thin radical of the distinguished basis of the table algebra has order p2, is resolved. The algebras in this case are explicitly determined up to isomorphism as wreath products, partial wreath products, or as members of a more complex family called hexagonal standard table algebras. These are parametrized by certain correspondences introduced in this article called hexagonal functions, that are defined in general from a subset of a group to an arbitrary set.