Homomorphisms of matrix algebras and constructions of Butson-Hadamard matrices

Padraig O Cathain, Eric Swartz

An $n\times n$ matrix $H$ is Butson-Hadamard if its entries are $k^{\text{th}}$ roots of unity and it satisfies $H{H}^{\ast }=n{I}_n$. Write $BH(n,k)$ for the set of such matrices. Suppo…