Loewy Structure as a q-analog of Composition Factors (Research on finite groups and their representations, vertex operator algebras, and algebraic combinatorics)

Abstract

The Loewy structure of a module can be viewed as a q-analog of its composition factors. From this point of view we define q-composition multiplicity; q-composition length, and the q-Cartan matrix. By way of example, group algebras of finite p-groups and path algebras of finite acyclic quivers are investigated. Some known results for these algebras are stated in terms of the q-Cartan matrix.