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Algebras of Linear Transformations

  • Douglas R. Farenick

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Douglas R. Farenick
    Pages 1-37
  3. Douglas R. Farenick
    Pages 39-75
  4. Douglas R. Farenick
    Pages 77-116
  5. Douglas R. Farenick
    Pages 117-149
  6. Douglas R. Farenick
    Pages 151-191
  7. Douglas R. Farenick
    Pages 193-232
  8. Back Matter
    Pages 233-239

About this book

Introduction

The aim of this book is twofold: (i) to give an exposition of the basic theory of finite-dimensional algebras at a levelthat isappropriate for senior undergraduate and first-year graduate students, and (ii) to provide the mathematical foundation needed to prepare the reader for the advanced study of anyone of several fields of mathematics. The subject under study is by no means new-indeed it is classical­ yet a book that offers a straightforward and concrete treatment of this theory seems justified for several reasons. First, algebras and linear trans­ formations in one guise or another are standard features of various parts of modern mathematics. These include well-entrenched fields such as repre­ sentation theory, as well as newer ones such as quantum groups. Second, a study ofthe elementary theory offinite-dimensional algebras is particularly useful in motivating and casting light upon more sophisticated topics such as module theory and operator algebras. Indeed, the reader who acquires a good understanding of the basic theory of algebras is wellpositioned to ap­ preciate results in operator algebras, representation theory, and ring theory. In return for their efforts, readers are rewarded by the results themselves, several of which are fundamental theorems of striking elegance.

Keywords

Multilinear Algebra algebra field linear algebra operator algebra representation theory transformation

Authors and affiliations

  • Douglas R. Farenick
    • 1
  1. 1.Department of MathematicsUniversity of ReginaReginaCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0097-7
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-95062-4
  • Online ISBN 978-1-4613-0097-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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