Representation Theory of Finite Monoids

• Κύριος συγγραφέας: Steinberg, Benjamin (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Σειρά: Universitext,
• Θέματα: Mathematics.; Group theory.; Probabilities.; Combinatorics.; Group Theory and Generalizations.; Probability Theory and Stochastic Processes.

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....

Πίνακας περιεχομένων:

• 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.