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K-Theory for group C*-Algebras and semigroup C*-Algebras [electronic resource]

K-Theory for group C*-Algebras and semigroup C*-Algebras [electronic resource]

Material type
E-Book(소장)
Personal Author
Cuntz, Joachim.
Title Statement
K-Theory for group C*-Algebras and semigroup C*-Algebras [electronic resource] / Joachim Cuntz, Siegfried Echterhoff, Xin Li, Guoliang Yu.
Publication, Distribution, etc
Cham :   Springer,   c2017.  
Physical Medium
1 online resource (x, 322 p.).
Series Statement
Oberwolfach Seminars,1661-237X ; 47
ISBN
9783319599144 9783319599151 (e-book)
요약
This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions.
General Note
Title from e-Book title page.  
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
K-theory. Functional analysis. Global analysis.
Short cut
URL
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020 ▼a 9783319599144
020 ▼a 9783319599151 (e-book)
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050 4 ▼a QA612.33
082 0 4 ▼a 512.66 ▼2 23
084 ▼a 512.66 ▼2 DDCK
090 ▼a 512.66
100 1 ▼a Cuntz, Joachim.
245 1 0 ▼a K-Theory for group C*-Algebras and semigroup C*-Algebras ▼h [electronic resource] / ▼c Joachim Cuntz, Siegfried Echterhoff, Xin Li, Guoliang Yu.
260 ▼a Cham : ▼b Springer, ▼c c2017.
300 ▼a 1 online resource (x, 322 p.).
490 1 ▼a Oberwolfach Seminars, ▼x 1661-237X ; ▼v 47
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
520 ▼a This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a K-theory.
650 0 ▼a Functional analysis.
650 0 ▼a Global analysis.
830 0 ▼a Oberwolfach Seminars ; ▼v 47.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-3-319-59915-1
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

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No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.66 Accession No. E14015383 Availability Loan can not(reference room) Due Date Make a Reservation Service M

Contents information

Table of Contents

Chapter 1: Introduction
Chapter 2: Crossed Products and the Mackey-Rieffel-Green machine
2.1 Introduction
2.2 some Preliminaries
2.2.1 C*-algebras
2.2.2 Multiple algebras
2.2.3 commutative C*-algebras and functional Calculus
2.2.4 Representation and ideal Spaces of C*-algebras
2.2.5 Tensor Products
2.3 Action and their Crossed Products
2.3.1 Hear measure and vector-Valued integration on groups
2.3.2 C*-dynamical systms and their crossed products
2.4 Crossed Products Versus tensor products
2.5 The Correspondence Categories
2.5.1 Hilbert Modules
2.5.2 Morita Equivalences
2.5.3 The correspondense categories
2.5.4 The equivariant Correspondence Categories
2.5.5 Induced Representation and ideals
2.5.6 the Fell topologies and weak containment
2.6 Green’s imprimitivity theorem and applications
2.6.1 The imprimitivity theorem
2.6.2 The Takesaki–Takai duality theorem
2.6.3 Permanence properties of exact groups
2.7 Induced representations and the ideal structure of crossed products
2.7.1 Induced representations of groups and crossed products
2.7.2 The ideal structure of crossed products
2.7.3 The Mackey machine for transformation groups
2.8 The Mackey–Rieffel–Green machine for twisted crossed products
2.8.1 Twisted actions and twisted crossed products
2.8.2 The twisted equivariant correspondence category and the stabilisation trick
2.8.3 Twisted Takesaki–Takai duality
2.8.4 Stability of exactness under group extensions
2.8.5 Induced representations of twisted crossed products
2.8.6 Twisted group algebras, actions on K and Mackey''s little group method
Chapter 3: Bivariant kk-Theory and the Baum–Connes conjecure
3.1 Introduction
3.2 Operator K-Theory
3.3 Kasparov’s equivariant KK-theory
3.3.1 Graded C* -algebras and Hilbert modules
3.3.2 Kasparov’s bivariant K-groups
3.3.3 The Kasparov product
3.3.4 Higher KK-groups and Bott-periodicity
3.3.5 Excision in KK-theory
3.4 The Baum–Connes conjecture
3.4.1 The universal proper G-space
3.4.2 The Baum–Connes assembly map
3.4.3 Proper G-algebras and the Dirac dual-Dirac method
3.4.4 The Baum–Connes conjecture for group extensions
3.5 The going-down (or restriction) principle and applications
3.5.1 The going-down principle
3.5.2 Applications of the going-down principle
3.5.3 Crossed products by actions on totally disconnected spaces
Chapter 4: Quantitative K-theory for geometric operator algebras
4.1 Introduction
4.2 Geometric C*-algebras
4.3 Quantitative K-theory for C*-algebras
4.4 A quantitative Mayer–Vietoris sequence
4.5 Dynamic asymptotic dimension and theory of crossed product C*-algebras
4.6 Asymptotic dimension for geometric C*-algebras and the K¨unneth formula
4.7 Quantitative K-theory for Banach algebras
Chapter 5: Semigroup C*-algebras
5.1 Introduction
5.2 C*-algebras generated by left regular representations
5.3 Examples
5.3.1 The natural numbers
5.3.2 Positive cones in totally ordered groups
5.3.3 Monoids given by presentations
5.3.4 Examples from rings in general, and number theory in particular
5.3.5 Finitely generated abelian cancellative semigroups
5.4 Preliminaries
5.4.1 Embedding semigroups into groups
5.4.2 Graph products
5.4.3 Krull rings
5.5 C*-algebras attached to inverse semigroups, partial dynamical systems and groupoids
5.5.1 Inverse semigroups
5.5.2 Partial dynamical systems
5.5.3 Étale groupoids
5.5.4 The universal groupoid of an inverse semigroup
5.5.5 Inverse semigroup C*-algebras as groupoid C*-algebras
5.5.6 C*-algebras of partial dynamical systems as C*-algebras of partial transformation groupoids
5.5.7 The case of inverse semigroups admitting an idempotent pure partial homomorphism to a group
5.6 Amenability and nuclearity
5.6.1 Groups and groupoids
5.6.2 Amenability for semigroups
5.6.3 Comparing reducedn C*-algebras for left cancellative semigroups and their left inverse hulls
5.6.4 C*-algebras generated by semigroups of projections
5.6.5 The independence condition
5.6.6 Construction of full semigroup C*-algebras
5.6.7 Crossed product and groupoid C*-algebra descriptions of reduced semigroup C*-algebras
5.6.8 Amenability of semigroups in terms of C*-algebras
5.6.9 Nuclearity of semigroup C*-algebras and the connection to amenability
5.7 Topological freeness, boundary quotients, and c* simplicity
5.8 The Toeplitz condition
5.9 Graph products
5.9.1 Constructible right ideals
5.9.2 The independence condition
5.9.3 The Toeplitz condition
5.10 K-theory
5.11 Further developments, outlook, and open questions
Chapter 6: Algebraic actions and their C*-algebras
6.1 Introduction
6.2 Single algebraic endomorphisms
6.2.1 The K-theory of U[φ]
6.2.2 Examples
6.3 Actions by a family of endomorphisms, ring C*-algebras
6.4 Regular C*-algebras for ax+b -semigroups
6.5 The K-theory for C*λ(RxRx)
6.6 KMS-States
Chapter 7: Semigroup C*-algebras and toric varieties
7.1 Introduction
7.2 Toric varieties
7.3 The regular C*-algebras for a toric semigroup

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