سیستم‌های دینامیکی جزئی، بسته‌های فِل و کاربردها (بررسی‌ها و مونوگراف‌های ریاضی)

Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C•-contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsaturated graded algebras which are in fact the source of the notion of “partiality”. One of the main results of the book states that every graded algebra satisfying suitable conditions may be reconstructed from a partial dynamical system via a process called the partial crossed product. Running in parallel with partial dynamical systems, partial representations of groups are also presented and studied in depth. In addition to presenting main theoretical results, several specific examples are analyzed, including Wiener–Hopf algebras and graph C•-algebras. Cover......Page 1 Title page......Page 4 Contents......Page 6 Chapter 1. Introduction......Page 8 Part 1 . Partial Actions......Page 10 Chapter 2. Partial Actions......Page 12 Chapter 3. Restriction and Globalization......Page 18 Chapter 4. Inverse Semigroups......Page 22 Chapter 5. Topological Partial Dynamical Systems......Page 26 Chapter 6. Algebraic Partial Dynamical Systems......Page 32 Chapter 7. Multipliers......Page 42 Chapter 8. Crossed Products......Page 46 Chapter 9. Partial Group Representations......Page 54 Chapter 10. Partial Group Algebras......Page 62 Chapter 11. C*-Algebraic Partial Dynamical Systems......Page 68 Chapter 12. Partial Isometries......Page 72 Chapter 13. Covariant Representations of C*-Algebraic Dynamical Systems......Page 90 Chapter 14. Partial Representations Subject to Relations......Page 98 Chapter 15. Hilbert Modules and Morita-Rieffel-Equivalence......Page 108 Part 2 . Fell Bundles......Page 116 Chapter 16. Fell Bundles......Page 118 Chapter 17. Reduced Cross-Sectional Algebras......Page 130 Chapter 18. Fell’s Absorption Principle......Page 140 Chapter 19. Graded C*-Algebras......Page 146 Chapter 20. Amenability for Fell Bundles......Page 152 Chapter 21. Functoriality for Fell Bundles......Page 160 Chapter 22. Functoriality for Partial Actions......Page 176 Chapter 23. Ideals in Graded Algebras......Page 182 Chapter 24. Pre-Fell-Bundles......Page 188 Chapter 25. Tensor Products of Fell Bundles......Page 194 Chapter 26. Smash Product......Page 204 Chapter 27. Stable Fell Bundles as Partial Crossed Products......Page 210 Chapter 28. Globalization in the C*-Context......Page 220 Chapter 29. Topologically Free Partial Actions......Page 232 Part 3 . Applications......Page 240 Chapter 30. Dilating Partial Representations......Page 242 Chapter 31. Semigroups of Isometries......Page 246 Chapter 32. Quasi-Lattice Ordered Groups......Page 254 Chapter 33. C*-Algebras Generated by Semigroups of Isometries......Page 266 Chapter 34. Wiener-Hopf C*-Algebras......Page 270 Chapter 35. The Toeplitz C*-Algebra of a Graph......Page 282 Chapter 36. Path Spaces......Page 292 Chapter 37. Graph C*-Algebras......Page 304 Bibliography......Page 320 Index......Page 326 Back Cover......Page 330 Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C" contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsaturated graded algebras which are in fact the source of the notion of "partiality". One of the main results of the book states that every graded algebra satisfying suitable conditions may be reconstructed from a partial dynamical system via a process called the partial crossed product. Running in parallel with partial dynamical systems, partial representations of groups are also presented and studied in depth. In addition to presenting main theoretical results, several specific examples are analyzed, including Wiener-Hopf algebras and graph C" algebras Part 1. Partial Actions -- Part 2. Fell Bundles -- Part 3. Applications. Ruy Exel. Includes Bibliographical References (pages 313-317) And Subject Index.