Analysis and Quantum Groups
暫譯: 分析與量子群

Tuset, Lars

Analysis and Quantum Groups
  • 出版商: Springer
  • 出版日期: 2022-07-28
  • 售價: $4,120
  • 貴賓價: 9.5 折 $3,914
  • 語言: 英文
  • 頁數: 544
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031072456
  • ISBN-13: 9783031072451
  • 相關分類: 量子 Quantum

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This volume presents a completely self-contained introduction to the elaborate theory of locally compact quantum groups, bringing the reader to the frontiers of present-day research. The exposition includes a substantial amount of material on functional analysis and operator algebras, subjects which in themselves have become increasingly important with the advent of quantum information theory. In particular, the rather unfamiliar modular theory of weights plays a crucial role in the theory, due to the presence of 'Haar integrals' on locally compact quantum groups, and is thus treated quite extensively

The topics covered are developed independently, and each can serve either as a separate course in its own right or as part of a broader course on locally compact quantum groups. The second part of the book covers crossed products of coactions, their relation to subfactors and other types of natural products such as cocycle bicrossed products, quantum doubles and doublecrossed products. Induced corepresentations, Galois objects and deformations of coactions by cocycles are also treated. Each section is followed by a generous supply of exercises. To complete the book, an appendix is provided on topology, measure theory and complex function theory.


商品描述(中文翻譯)

本卷提供了一個完全自足的介紹，深入探討局部緊湊量子群的複雜理論，將讀者帶到當前研究的前沿。該論述包含了大量有關函數分析和算子代數的材料，這些主題隨著量子信息理論的興起而變得越來越重要。特別是，相對不熟悉的權重模組理論在該理論中扮演了關鍵角色，因為在局部緊湊量子群上存在「Haar 積分」，因此這部分內容得到了相當廣泛的討論。

所涵蓋的主題是獨立發展的，每個主題都可以作為一門獨立的課程，或作為局部緊湊量子群更廣泛課程的一部分。本書的第二部分涵蓋了共作用的交叉乘積、它們與子因子及其他類型的自然乘積（如共循環雙交叉乘積、量子雙重和雙重交叉乘積）之間的關係。還討論了誘導共表示、伽羅瓦物件以及通過共循環的共作用變形。每個部分後面都有豐富的練習題。為了補充本書，還提供了一個有關拓撲學、測度論和複變函數理論的附錄。

作者簡介

Lars Tuset is Professor of Mathematics at Oslo Metropolitan University. He has worked actively in the area of operator algebras and quantum groups since locally compact quantum groups were introduced in the 90's, and offers firsthand experience of the development of the theory with all its pros and cons. He has previously published a monograph on compact quantum groups and their representation categories.

His research includes amenability of locally compact quantum groups, and cocycle deformations of coactions of locally compact quantum groups in the context of crossed products.

作者簡介(中文翻譯)

拉斯·圖塞特（Lars Tuset）是奧斯陸 metropolitan 大學的數學教授。他自1990年代局部緊湊量子群（locally compact quantum groups）被引入以來，積極從事算子代數（operator algebras）和量子群（quantum groups）領域的研究，並對該理論的發展及其優缺點有著第一手的經驗。他之前曾發表過一本關於緊湊量子群（compact quantum groups）及其表示類別（representation categories）的專著。

他的研究包括局部緊湊量子群的可容性（amenability），以及在交叉乘積（crossed products）背景下局部緊湊量子群的共同作用（coactions）之鍊（cocycle）變形（deformations）。

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