Orthogonality relation for Frobenius- and quasi-Frobenius-algebras

Abstract

The celebrated orthogonality relation for the coefficients of the regular representation of a group was extended first to the modular case by Nesbitt, and then to Frobenius-algebras by the writer; the proof was reproduced in [4]1 together with a second proof. Another proof of this orthogonality, for the coefficients of the regular representations of Frobenius-algebras, and its interesting application to faithful representations were given by Brauer [1]. In the present note we propose a still different proof, and generalize the orthogonality to quasiFrobenius-algebras. 1. A class of automorphisms in a Frobenius-algebra. Let 21 be a Frobenius-algebra [1; 2; 3; 4.] over a field Q, and let (1) (a1, a2, n, a) with aa ar =E as be its basis. Let