Introduction to Lie Algebras

Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. Based on a lecture course given to fourth-year undergraduates, this book provides an elementary introduction to Lie algebras. It...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Erdmann, K. (Autor), Wildon, Mark J. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London : Springer London : Imprint: Springer, 2006.
Edición:1st ed. 2006.
Colección:Springer Undergraduate Mathematics Series,
Temas:
Algebra.
Mathematical physics.
Theoretical, Mathematical and Computational Physics.
Mathematical Methods in Physics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Ideals and Homomorphisms
  • Low-Dimensional Lie Algebras
  • Solvable Lie Algebras and a Rough Classification
  • Subalgebras of gl(V)
  • Engel's Theorem and Lie's Theorem
  • Some Representation Theory
  • Representations of sl(2, C)
  • Cartan's Criteria
  • The Root Space Decomposition
  • Root Systems
  • The Classical Lie Algebras
  • The Classification of Root Systems
  • Simple Lie Algebras
  • Further Directions
  • Appendix A: Linear Algebra
  • Appendix B: Weyl's Theorem
  • Appendix C: Cartan Subalgebras
  • Appendix D: Weyl Groups
  • Appendix E: Answers to Selected Exercises.

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