An Introduction to Groups, Groupoids and Their Representations
暫譯: 群、群體及其表示的入門介紹

Ibort, Alberto, Rodriguez, Miguel A.

An Introduction to Groups, Groupoids and Their Representations
  • 出版商: CRC
  • 出版日期: 2019-11-04
  • 售價: $5,870
  • 貴賓價: 9.5 折 $5,577
  • 語言: 英文
  • 頁數: 18
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1138035866
  • ISBN-13: 9781138035867

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商品描述

This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject.

Category theory is the natural language that is being used to develop the theory of groupoids. However, categorical presentations of mathematical subjects tend to become highly abstract very fast and out of reach of many potential users. To avoid this, foundations of the theory, starting with simple examples, have been developed and used to study the structure of finite groups and groupoids. The appropriate language and notions from category theory have been developed for students of mathematics and theoretical physics. The book presents the theory on the same level as the ordinary and elementary theories of finite groups and their representations, and provides a unified picture of the same. The structure of the algebra of finite groupoids is analysed, along with the classical theory of characters of their representations.

Unnecessary complications in the formal presentation of the subject are avoided. The book offers an introduction to the language of category theory in the concrete setting of finite sets. It also shows how this perspective provides a common ground for various problems and applications, ranging from combinatorics, the topology of graphs, structure of databases and quantum physics.

商品描述(中文翻譯)

這本書介紹了群體（groupoids）及其表示的理論，涵蓋了標準的群（groups）理論。使用從簡單範例發展而來的範疇語言，有限群體的理論與群及其結構緊密相連，並描述了它們的表示。書中包含了許多範例和應用，包括知名的遊戲和謎題、資料庫以及物理應用。關鍵概念僅使用基本概念呈現，以便學生和對該主題感興趣的研究人員都能使用。

範疇理論是用來發展群體理論的自然語言。然而，數學主題的範疇表述往往會迅速變得高度抽象，讓許多潛在使用者無法接觸。為了避免這種情況，理論的基礎從簡單範例開始發展，並用來研究有限群和群體的結構。適合數學和理論物理學生的範疇理論語言和概念已經被發展出來。這本書在與有限群及其表示的普通和基本理論相同的層次上呈現理論，並提供了一個統一的視角。有限群體的代數結構被分析，並與其表示的經典角色理論相結合。

在主題的正式表述中避免不必要的複雜性。這本書在有限集合的具體背景下介紹了範疇理論的語言。它還展示了這種視角如何為各種問題和應用提供共同的基礎，涵蓋了組合學、圖的拓撲、資料庫結構和量子物理等領域。

作者簡介

Alberto Ibort is full professor of Applied Mathematics in the Department of Mathematics of the Universidad Carlos III of Madrid, Spain and member of the Mathematical Institute, ICMAT, Madrid, Spain. He has been visiting professor and Fulbright Scholar at the University of California at Berkeley, USA, postdoc at the Université de Paris VI, France and the Niels Bohr Institute, Denmark, and professor of Theoretical Physics at the Universidad Complutense of Madrid. His research includes several areas of Mathematics and Mathematical Physics: Functional Analysis, Differential Geometry and more recently algebraic structures on Physics and Engineering, mainly control theory.

Miguel A. Rodríguez is full professor in the Department of Theoretical Physics of Universidad Complutense of Madrid, Spain. His teaching is mainly related to courses on　Mathematics applied to Physics, in particular group theory. He has been visiting professor at Université de Montréal, Canada, University of California at Los Angeles, USA, and Università di Roma Tre, Italy. His research field includes several areas of Mathematical Physics: Integrable Systems, Group Theory, and Difference Equations.

作者簡介(中文翻譯)

阿爾貝托·伊博特是西班牙馬德里卡洛斯三世大學數學系的應用數學全職教授，也是馬德里數學研究所（ICMAT）的成員。他曾擔任美國加州大學伯克利分校的訪問教授和富布賴特學者，並在法國巴黎第六大學和丹麥尼爾斯·玻爾研究所擔任博士後研究員，還曾是馬德里康普頌斯大學的理論物理教授。他的研究涵蓋數學和數學物理的幾個領域：泛函分析、微分幾何，以及最近在物理和工程中的代數結構，主要是控制理論。

米格爾·A·羅德里格斯是西班牙馬德里康普頌斯大學理論物理系的全職教授。他的教學主要與應用於物理的數學課程有關，特別是群論。他曾在加拿大蒙特利爾大學、美國加州大學洛杉磯分校和意大利羅馬三大學擔任訪問教授。他的研究領域包括數學物理的幾個領域：可積系統、群論和差分方程。

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