Exel R. Partial Dynamical Systems, Fell Bundles and Applications

American Mathematical Society, 2017. — 330 p. — (Mathematical Surveys and Monographs 224). — ISBN: 1470437856.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.Partial Actions
Partial Actions
Restriction and Globalization
Inverse Semigroups
Topological Partial Dynamical Systems
Algebraic Partial Dynamical Systems
Multipliers
Crossed Products
Partial Group Representations
Partial Group Algebras
C*-Algebraic Partial Dynamical Systems
Partial Isometries
Covariant Representations of C*-Algebraic Dynamical Systems
Partial Representations Subject to Relations
Hilbert Modules and Morita-Rieffel-Equivalence
Fell Bundles
Fell Bundles
Reduced Cross-Sectional Algebras
Absorption Principle
Graded C*-Algebras
Amenability for Fell Bundles
Functoriality for Fell Bundles
Functoriality for Partial Actions
Ideals in Graded Algebras
Pre-Fell-Bundles
Products of Fell Bundles
Smash Product
Stable Fell Bundles as Partial Crossed Products
Globalization in the C*-Context
Topologically Free Partial Actions
Applications
Dilating Partial Representations of Isometries
Quasi-Lattice Ordered Groups
*-Algebras Generated by Semigroups of Isometries
Wiener-Hopf C*-Algebras
The Toeplitz C*-Algebra of a Graph
Path Spaces
Graph C*-Algebras