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eBook ISBN: | 978-1-4704-4236-1 |
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Hardcover ISBN: | 978-1-4704-3785-5 |
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Hardcover ISBN: | 978-1-4704-3785-5 |
Product Code: | SURV/224 |
List Price: | $129.00 |
MAA Member Price: | $116.10 |
AMS Member Price: | $103.20 |
eBook ISBN: | 978-1-4704-4236-1 |
Product Code: | SURV/224.E |
List Price: | $125.00 |
MAA Member Price: | $112.50 |
AMS Member Price: | $100.00 |
Hardcover ISBN: | 978-1-4704-3785-5 |
eBook ISBN: | 978-1-4704-4236-1 |
Product Code: | SURV/224.B |
List Price: | $254.00 $191.50 |
MAA Member Price: | $228.60 $172.35 |
AMS Member Price: | $203.20 $153.20 |
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Book DetailsMathematical Surveys and MonographsVolume: 224; 2017; 321 ppMSC: Primary 46; 37; 16
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.
ReadershipGraduate students and researchers interested in C*-algebras and dynamical systems.
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Table of Contents
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Chapters
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Introduction
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Partial actions
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Partial actions
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Restriction and globalization
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Inverse semigroups
-
Topological partial dynamical sysytems
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Algebraic partial dynamical systems
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Multipliers
-
Crossed products
-
Partial group representations
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Partial group algebras
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C*-algebraic partial dynamical systems
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Partial isometries
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Covariant representations of C*-algebraic dynamical systems
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Partial representations subject to relations
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Hilbert modules and Morita-Rieffel-equivalence
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Fell bundles
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Fell bundles
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Reduced cross-sectional algebras
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Fell’s absorption principle
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Graded C*-algebras
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Amenability for Fell bundles
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Functoriality for Fell bundles
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Functoriality for partial actions
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Ideals in graded algebras
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Pre-Fell-bundles
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Tensor products of Fell bundles
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Smash product
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Stable Fell bundles as partial crossed products
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Globalization in the C*-context
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Topologically free partial actions
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Applications
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Dilating partial representations
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Semigroups of isometries
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Quasi-lattice ordered groups
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C*-algebras generated by semigroups of isometries
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Wiener-Hopf C*-algebras
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The Toeplitz C*-algebra of a graph
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Path spaces
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Graph C*-algebras
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Additional Material
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Reviews
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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
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
Graduate students and researchers interested in C*-algebras and dynamical systems.
-
Chapters
-
Introduction
-
Partial actions
-
Partial actions
-
Restriction and globalization
-
Inverse semigroups
-
Topological partial dynamical sysytems
-
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
-
Fell’s absorption principle
-
Graded C*-algebras
-
Amenability for Fell bundles
-
Functoriality for Fell bundles
-
Functoriality for partial actions
-
Ideals in graded algebras
-
Pre-Fell-bundles
-
Tensor 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
-
Semigroups of isometries
-
Quasi-lattice ordered groups
-
C*-algebras generated by semigroups of isometries
-
Wiener-Hopf C*-algebras
-
The Toeplitz C*-algebra of a graph
-
Path spaces
-
Graph C*-algebras
-
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