Characterizing Groupoid C*-Algebras of Non-Hausdorff Etale Groupoids
暫譯: 非豪斯多夫展開群體的群體 C*-代數特徵化

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: $2,230
  • 貴賓價: 9.5 折 $2,119
  • 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)

這本書開發了處理 C*-代數的工具，這些代數是作為可能非豪斯多夫群體的線束截面的卷積代數的完備化。Gelfand 的一個基本結果描述了可交換的 C*-代數作為在局部緊豪斯多夫空間上的連續函數。

Kumjian，後來的 Renault，顯示 Gelfand 的結果可以擴展到包括包含可交換 C*-代數的非可交換 C*-代數。在他們的設定中，所討論的 C*-代數可以描述為在扭曲豪斯多夫群體上相對於某個範數的函數的卷積代數的完備化。然而，在許多自然的情境中，Kumjian-Renault 理論並不適用，部分原因是所產生的群體不是豪斯多夫的。事實上，非豪斯多夫群體幾十年來一直是驚人反例和技術困難的來源。本書包含了許多說明性例子，將 Kumjian-Renault 理論擴展到更廣泛的 C*-代數類別。

這項工作將對研究群體 C*-代數、動態系統與 C*-代數之間的接口以及相關領域的研究人員和研究生感興趣。

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的研究，特別強調其與動態系統和數學物理的互動。他是群對 C*-代數的部分作用領域的先驅，最近出版了《Partial Dynamical Systems, Fell Bundles and Applications》一書。他曾是2018年里約國際數學家大會的受邀演講者。

David R. Pitts 是內布拉斯加州林肯大學的數學教授。他在算子代數的各個方面發表了研究，包括：可交換子空間格代數、自由半群代數，以及冯·諾伊曼代數和 C*-代數的卡坦子代數。

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