Partial Dynamical Systems, Fell Bundles and Applications

TL;DR

This comprehensive book explores partial dynamical systems, Fell bundles, and their applications to C*-algebras, providing theoretical foundations, constructions, and examples in operator algebra theory.

Contribution

It offers a detailed synthesis of partial actions, Fell bundles, and their applications to C*-algebras, including new results on globalization, graded algebras, and crossed products.

Findings

Development of globalization techniques for partial actions

Introduction of new classes of Fell bundles and their properties

Applications to C*-algebras generated by partial isometries

Abstract

This is a book about Partial Actions and Fell Bundles with applications to C*-algebras generated by partial isometries. Here is the table of contents: 1-Introduction, 2-Partial actions, 3-Restriction and globalization, 4-Inverse semigroups, 5-Topological partial dynamical systems, 6-Algebraic partial dynamical systems, 7-Multipliers, 8-Crossed products, 9-Partial group representations, 10-Partial group algebras, 11-C*-algebraic partial dynamical systems, 12-Partial isometries, 13-Covariant representations of C*-algebraic dynamical systems, 14-Partial representations subject to relations, 15-Hilbert modules and Morita-Rieffel-equivalence, 16-Fell bundles, 17-Reduced cross-sectional algebras, 18-Fell's absorption principle, 19-Graded C*-algebras, 20-Amenability for Fell bundles, 21-Functoriality for Fell bundles, 22-Functoriality for partial actions, 23-Ideals in graded algebras, 24-Pre-Fell-bundles, 25-Tensor products of Fell bundles, 26-Smash product, 27-Stable Fell bundles as partial crossed products, 28-Globalization in the C*-context, 29-Topologically free partial actions, 30-Dilating partial representations, 31-Semigroups of isometries, 32-Quasi-lattice ordered groups, 33-C*-algebras generated by semigroups of isometries, 34-Wiener-Hopf C*-algebras, 35-The Toeplitz C*-algebra of a graph, 36-Path spaces, 37-Graph C*-algebras, 38-References, 39-Subject Index.