Finite Dimensional Algebras

  • Yurij A. Drozd
  • Vladimir V. Kirichenko

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 1-30
  3. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 31-43
  4. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 44-68
  5. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 69-81
  6. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 82-103
  7. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 104-116
  8. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 117-134
  9. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 135-158
  10. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 159-173
  11. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 174-189
  12. Yurij A. Drozd, Vladimir V. Kirichenko
    Pages 190-211
  13. Back Matter
    Pages 212-249

About this book

Introduction

This English edition has an additional chapter "Elements of Homological Al­ gebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only metic­ ulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface The theory of finite dimensional algebras is one of the oldest branches of modern algebra. Its origin is linked to the work of Hamilton who discovered the famous algebra of quaternions, and Cayley who developed matrix theory. Later finite dimensional algebras were studied by a large number of mathematicians including B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. At the end of the last century T. Molien and E. Cartan described the semisimple algebras over the complex and real fields and paved the first steps towards the study of non-semi simple algebras.

Keywords

Algebras Algebren (endlichdimensionale) Darstellungstheorie Galois group Galois theory Group theory Vector space algebra category theory finite group homological algebra homologische Algebra representation theory

Authors and affiliations

  • Yurij A. Drozd
    • 1
  • Vladimir V. Kirichenko
    • 1
  1. 1.Faculty of Mechanics and MathematicsKiev Taras Shevchenko UniversityKievUkraina

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-76244-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-76246-8
  • Online ISBN 978-3-642-76244-4
  • About this book