Representation Theory of Finite Monoids

This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area....

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Steinberg, Benjamin (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edición:1st ed. 2016.
Colección:Universitext,
Temas:
Group theory.
Probabilities.
Discrete mathematics.
Group Theory and Generalizations.
Probability Theory.
Discrete Mathematics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Preface
  • List of Figures
  • Introduction
  • I. Elements of Monoid Theory
  • 1. The Structure Theory of Finite Monoids
  • 2. R-trivial Monoids
  • 3. Inverse Monoids
  • II. Irreducible Representations
  • 4. Recollement: The Theory of an Idempotent
  • 5. Irreducible Representations
  • III. Character Theory
  • 6. Grothendieck Ring
  • 7. Characters and Class Functions
  • IV. The Representation Theory of Inverse Monoids
  • 8. Categories and Groupoids
  • 9. The Representation Theory of Inverse Monoids
  • V. The Rhodes Radical
  • 10. Bi-ideals and R. Steinberg's Theorem
  • 11. The Rhodes Radical and Triangularizability
  • VI. Applications
  • 12. Zeta Functions of Languages and Dynamical Systems
  • 13. Transformation Monoids
  • 14. Markov Chains
  • VII. Advanced Topics
  • 15. Self-injective, Frobenius and Symmetric Algebras
  • 16. Global Dimension
  • 17. Quivers of Monoid Algebras
  • 18. Further Developments
  • A. Finite Dimensional Algebras
  • B. Group Representation Theory
  • C. Incidence Algebras and Möbius Inversion
  • References
  • Index of Notation
  • Subject Index.

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