On the wedge product of table algebras and applications to association schemes

TL;DR

This paper generalizes the wedge product concept from association schemes to table algebras, providing conditions for such products and exploring their duals, with applications to association schemes.

Contribution

It introduces a new framework for wedge products of table algebras and characterizes when a table algebra can be expressed as such a product.

Findings

A necessary and sufficient condition for a table algebra to be a wedge product.

Duals of wedge products of commutative table algebras are also table algebras.

Applications to association schemes are demonstrated.

Abstract

In this paper we will first present a generalization of the wedge product of association schemes to table algebras and give a necessary and sufficient condition for a table algebra to be the wedge product of two table algebras. Then we show that if the duals of two commutative table algebras are table algebras, then the dual of their wedge product is a table algebra, and is also isomorphic to the wedge product of the duals of those table algebras in the reverse order. Some applications to association schemes are also given.