Twisted Orthogonality Relations For Certain $\mathbb{Z}/m\mathbb{Z}$-graded Algebras

Abstract

In this paper we will study the notion of a Frobenius $\star$-algebra and prove some orthogonality relations for the irreducible characters of a Frobenius $\star$-algebra. Then we will study $\mathbb{Z}/m\mathbb{Z}$-graded Frobenius $\star$- algebras and prove some twisted orthogonality relations for them.