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Mathematics - Algebra | Representing Finite Groups - A Semisimple Introduction

Representing Finite Groups

A Semisimple Introduction

Sengupta, Ambar N.

2012, XVI, 372 p.

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  • Presents basics of representation theory of finite groups from the point of view of semisimple algebras and modules over them
  • Progresses systematically with a gentle and inviting pace
  • Exercises at the end of the chapter help reinforce the material

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.

Content Level » Graduate

Keywords » group algebra - group theory - quantum physics - semisimple algebras

Related subjects » Algebra - Applications - Quantum Physics - Theoretical, Mathematical & Computational Physics

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