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Hardcover ISBN:  9781470437855 
Product Code:  SURV/224 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470442361 
Product Code:  SURV/224.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9781470437855 
eBook ISBN:  9781470442361 
Product Code:  SURV/224.B 
List Price:  $254.00 $191.50 
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AMS Member Price:  $203.20 $153.20 

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.

Table of Contents

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 MoritaRieffelequivalence

Fell bundles

Fell bundles

Reduced crosssectional algebras

Fell’s absorption principle

Graded C*algebras

Amenability for Fell bundles

Functoriality for Fell bundles

Functoriality for partial actions

Ideals in graded algebras

PreFellbundles

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

Quasilattice ordered groups

C*algebras generated by semigroups of isometries

WienerHopf C*algebras

The Toeplitz C*algebra of a graph

Path spaces

Graph C*algebras


Additional Material

Reviews

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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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 MoritaRieffelequivalence

Fell bundles

Fell bundles

Reduced crosssectional algebras

Fell’s absorption principle

Graded C*algebras

Amenability for Fell bundles

Functoriality for Fell bundles

Functoriality for partial actions

Ideals in graded algebras

PreFellbundles

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

Quasilattice ordered groups

C*algebras generated by semigroups of isometries

WienerHopf 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