Semisimple Commutative Algebras with Positive Bases

Algebras that serve as models for concurrent studying of certain aspects of both the algebra of ordinary characters and the center of the group algebra of a finite group have been considered by various authors. In this article we offer another such model. The main differences between our model and the known ones are: 1. Our model includes Brauer characters and principal indecomposable characters as special cases. 2. Our emphasis is on the eigenvalues of the regular representation of the algebra elements, an approach that gives results on values of characters (ordinary, central, Brauer, principal indecomposable) as well as on their products.