On the wedge product of table algebras and applications to association schemes
arXiv:1508.05604
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.
arXiv commentThis paper has been withdrawn by the author. The main results, a table algebra construction (called here wedge product) and its characterization (Theorems 3.2, 3.6) are already known. See Theorem 2.9 and Proposition 2.11 of [H. Blau, Fusion rings with few degrees, J. Algebra 396 (2013), 220-271]