Semi-Simple 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 have been considered by various authors. In this article we o¤er another such model. The main di¤erences 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. Supported by the fund for the promotion of research at the Technion.