**Mathematical Surveys and Monographs**

Volume: 224;
2017;
321 pp;
Hardcover

MSC: Primary 46; 37; 16;

**Print ISBN: 978-1-4704-3785-5
Product Code: SURV/224**

List Price: $116.00

AMS Member Price: $92.80

MAA Member Price: $104.40

**Electronic ISBN: 978-1-4704-4236-1
Product Code: SURV/224.E**

List Price: $116.00

AMS Member Price: $92.80

MAA Member Price: $104.40

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#### Supplemental Materials

# Partial Dynamical Systems, Fell Bundles and Applications

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*Ruy Exel*

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.

#### Readership

Graduate students and researchers interested in C*-algebras and dynamical systems.

#### Reviews & Endorsements

This is a very interesting book which, with clarity and a steady flow, takes the reader through some important topics in the field of modern operator algebras, highlighting both better known and newer insights.The author guides the reader along the carefully prepared path to acquire familiarity with the fundamental concepts in the first two parts, and to enjoy the rich interplay at hand, as is particularly evident in the applications part...The book will prove valuvable to graduate students and advanced researchers alike.

-- Nadia Larsen, Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Partial Dynamical Systems, Fell Bundles and Applications

- Cover Cover11
- Frontispiece ii3
- Title page iii4
- Copyright iv5
- Contents v6
- Introduction 18
- Partial actions 310
- Partial actions 512
- Restriction and globalization 1118
- Inverse semigroups 1522
- Topological partial dynamical sysytems 1926
- Algebraic partial dynamical systems 2532
- Multipliers 3542
- Crossed products 3946
- Partial group representations 4754
- Partial group algebras 5562
- C*-algebraic partial dynamical systems 6168
- Partial isometries 6572
- Covariant representations of C*-algebraic dynamical systems 8390
- Partial representations subject to relations 9198
- Hilbert modules and Morita-Rieffel-equivalence 101108
- Fell bundles 109116
- Fell bundles 111118
- Reduced cross-sectional algebras 123130
- Fell’s absorption principle 133140
- Graded C*-algebras 139146
- Amenability for Fell bundles 145152
- Functoriality for Fell bundles 153160
- Functoriality for partial actions 169176
- Ideals in graded algebras 175182
- Pre-Fell-bundles 181188
- Tensor products of Fell bundles 187194
- Smash product 197204
- Stable Fell bundles as partial crossed products 203210
- Globalization in the C*-context 213220
- Topologically free partial actions 225232
- Applications 233240
- Dilating partial representations 235242
- Semigroups of isometries 239246
- Quasi-lattice ordered groups 247254
- C*-algebras generated by semigroups of isometries 259266
- Wiener-Hopf C*-algebras 263270
- The Toeplitz C*-algebra of a graph 275282
- Path spaces 285292
- Graph C*-algebras 297304
- Bibliography 313320
- Index 319326
- Back Cover Back Cover1330