Crossed products by Hecke pairs / Rui Palma.

Format:

Book

Author/Creator:

Palma, Rui, 1985- author.

Series:

Memoirs of the American Mathematical Society ; Volume 252, Number 1204.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 252, Number 1204

Language:

English

Subjects (All):

Crossed products.

Hecke algebras.

Group algebras.

Non-Abelian groups.

C*-algebras.

Physical Description:

1 online resource (156 pages).

Edition:

1st ed.

Place of Publication:

Providence, RI : American Mathematical Society, [2018]

Summary:

The author develops a theory of crossed products by actions of Hecke pairs (G, \Gamma ), motivated by applications in non-abelian C^*-duality. His approach gives back the usual crossed product construction whenever G / \Gamma is a group and retains many of the aspects of crossed products by groups. The author starts by laying the ^*-algebraic foundations of these crossed products by Hecke pairs and exploring their representation theory and then proceeds to study their different C^*-completions. He establishes that his construction coincides with that of Laca, Larsen and Neshveyev whenever they are both definable and, as an application of his theory, he proves a Stone-von Neumann theorem for Hecke pairs which encompasses the work of an Huef, Kaliszewski and Raeburn.

Contents:

Cover

Title page

Introduction

Chapter 1. Preliminaries

1.1. *-Algebras and (pre-)*-representations

1.2. *-Algebraic multiplier algebras

1.3. Hecke algebras

1.4. Fell bundles over discrete groupoids

Chapter 2. Orbit space groupoids and Fell bundles

2.1. Group actions on Fell bundles

2.2. Examples

2.3. The algebra ( _{ }(\a))

Chapter 3. *-Algebraic crossed product by a Hecke pair

3.1. Definition of the crossed product and basic properties

3.2. Basic Examples

3.3. Representation theory

3.4. More on covariant pre-*-representations

3.5. Crossed product in the case of free actions

Chapter 4. Direct limits of sectional algebras

4.1. Reduced completions *ᵣ(\a/ )

4.2. Maximal completions *(\a/ )

Chapter 5. Reduced *-crossed products

5.1. Regular representations

5.2. Reduced *-crossed products

5.3. Alternative definition of ᵣ*(\a/\gm)×_{ , } /\gm

5.4. Comparison with Laca-Larsen-Neshveyev construction

Chapter 6. Other completions

6.1. Full *-crossed products

6.2. ¹-norm and associated *-completion

Chapter 7. Stone-Von Neumann Theorem For Hecke Pairs

Chapter 8. Towards Katayama duality

Bibliography

Index

Back Cover.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-4377-5