Characterizing Groupoid C*-Algebras of Non-Hausdorff Etale Groupoids

Exel, Ruy, Pitts, David

Characterizing Groupoid C*-Algebras of Non-Hausdorff Etale Groupoids
  • 出版商: Springer
  • 出版日期: 2022-10-20
  • 售價: $2,190
  • 貴賓價: 9.5 折 $2,081
  • 語言: 英文
  • 頁數: 120
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031055128
  • ISBN-13: 9783031055126

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商品描述

This book develops tools to handle C*-algebras arising as completions of convolution algebras of sections of line bundles over possibly non-Hausdorff groupoids. A fundamental result of Gelfand describes commutative C*-algebras as continuous functions on locally compact Hausdorff spaces.

Kumjian, and later Renault, showed that Gelfand's result can be extended to include non-commutative C*-algebras containing a commutative C*-algebra. In their setting, the C*-algebras in question may be described as the completion of convolution algebras of functions on twisted Hausdorff groupoids with respect to a certain norm. However, there are many natural settings in which the Kumjian-Renault theory does not apply, in part because the groupoids which arise are not Hausdorff. In fact, non-Hausdorff groupoids have been a source of surprising counterexamples and technical difficulties for decades. Including numerous illustrative examples, this book extends the Kumjian-Renault theory to a much broader class of C*-algebras.

This work will be of interest to researchers and graduate students in the area of groupoid C*-algebras, the interface between dynamical systems and C*-algebras, and related fields.

 

商品描述(中文翻譯)

本書開發了處理C*-代數的工具，這些代數是作為可能非Hausdorff群組上線束截面的卷積代數的完備。Gelfand的一個基本結果描述了可交換的C*-代數作為局部緊致Hausdorff空間上的連續函數。

Kumjian和後來的Renault表明，Gelfand的結果可以擴展到包含可交換C*-代數的非可交換C*-代數。在他們的設置中，所討論的C*-代數可以描述為對應於某種範數的扭曲Hausdorff群組上函數的卷積代數的完備。然而，有許多自然的情況下Kumjian-Renault理論不適用，部分原因是所涉及的群組不是Hausdorff。事實上，非Hausdorff群組數十年來一直是令人驚訝的反例和技術困難的來源。本書通過包含許多具體例子，將Kumjian-Renault理論擴展到更廣泛的C*-代數類別。

這項工作對於群組C*-代數領域、動力系統和C*-代數之間的界面以及相關領域的研究人員和研究生具有興趣。

作者簡介

Ruy Exel is a professor of Mathematics at the Universidade Federal de Santa Catarina, in Brazil. He has published extensively in the subject of operator algebras with emphasis on its interactions with dynamical systems and mathematical physics. A pioneer in the area of partial actions of groups on C*-algebras, he has recently published the book Partial Dynamical Systems, Fell Bundles and Applications. He was an invited speaker in the 2018 ICM in Rio.
David R. Pitts is a professor of mathematics at the University of Nebraska-Lincoln. He has published work on various aspects of operator algebras, including: commutative subspace lattice algebras, free semigroup algebras, and Cartan subalgebras of von Neumann algebras and C*-algebras.

 

作者簡介(中文翻譯)

Ruy Exel 是巴西聖卡塔琳娜聯邦大學的數學教授。他在算子代數領域發表了大量論文，並強調其與動力系統和數學物理的相互作用。作為群在C*-代數上的部分作用領域的先驅者，他最近出版了《部分動力系統，費爾束和應用》一書。他曾是2018年里約國際數學家大會的邀請演講嘉賓。

David R. Pitts 是內布拉斯加大學林肯分校的數學教授。他在算子代數的各個方面發表了論文，包括：交換子空間格代數、自由半群代數以及von Neumann代數和C*-代數的Cartan子代數。

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