Lie Groups, Lie Algebras, and Cohomology
eBook - PDF

Lie Groups, Lie Algebras, and Cohomology

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Lie Groups, Lie Algebras, and Cohomology

About this book

This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory.


These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.

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Yes, you can access Lie Groups, Lie Algebras, and Cohomology by Anthony W. Knapp in PDF and/or ePUB format, as well as other popular books in Mathematics & Abstract Algebra. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover Page
  2. Half-title Page
  3. Title Page
  4. Copyright Page
  5. Dedication Page
  6. Contents
  7. Preface
  8. Chapter I. Lie Groups and Lie Algebras
  9. Chapter II. Representations and Tensors
  10. Chapter III. Representations of Compact Groups
  11. Chapter IV. Cohomology of Lie Algebras
  12. Chapter V. Homological Algebra
  13. Chapter VI. Application to Lie Algebras
  14. Chapter VII. Relative Lie Algebra Cohomology
  15. Chapter VIII. Representations of Noncompact Groups
  16. Notes
  17. References
  18. Index of Notation
  19. Index