This graduate textbook presents the basics of representation theory
for finite groups from the point of view of semisimple algebras and
modules over them. The presentation interweaves insights from
specific examples with development of general and powerful tools
based on the notion of semisimplicity. The elegant ideas of
commutant duality are introduced, along with an introduction to
representations of unitary groups. The text progresses
systematically and the presentation is friendly and inviting.
Central concepts are revisited and explored from multiple
viewpoints. Exercises at the end of the chapter help reinforce the
material. Representing Finite Groups: A Semisimple Introduction
would serve as a textbook for graduate and some advanced
undergraduate courses in mathematics. Prerequisites include
acquaintance with elementary group theory and some familiarity with
rings and modules. A final chapter presents a self-contained
account of notions and results in algebra that are used.
Researchers in mathematics and mathematical physics will also find
this book useful. A separate solutions manual is available for
instructors.
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