Basic Algebraic Concepts for Group Representations

Abstract

We first collect the basic definitions and concepts concerning representations of groups, using only algebraic methods. As is common, we introduce the concept of a linear representation, which is completely adequate and sufficient for the study of representations of finite groups. In a later chapter we will enrich the discussion with elements from topology to refine the notion of a representation to that of a continuous representation. We start by stating the essential definitions and only afterwards illustrate these by some examples and constructions.