An Introduction to Hopf Algebras
暫譯: 霍夫代數入門

Underwood, Robert G.

An Introduction to Hopf Algebras
  • 出版商: Springer
  • 出版日期: 2011-08-30
  • 售價: $2,430
  • 貴賓價: 9.5 折 $2,308
  • 語言: 英文
  • 頁數: 273
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 0387727655
  • ISBN-13: 9780387727653
  • 相關分類: 離散數學 Discrete-mathematics

    • 海外代購書籍(需單獨結帳)

商品描述

With wide-ranging connections to fields from theoretical physics to computer science, Hopf algebras offer students a glimpse at the applications of abstract mathematics. This book is unique in making this engaging subject accessible to advanced undergraduate and beginning graduate students. After providing a self-contained introduction to group and ring theory, the book thoroughly treats the concept of the spectrum of a ring and the Zariski topology. In this way the student transitions smoothly from basic abstract algebra to Hopf algebras. The importance of Hopf orders is underscored with applications to algebraic number theory, Galois module theory and the theory of formal groups. By the end of the book, readers will be familiar with established results in the field and ready to pose research questions of their own.

商品描述(中文翻譯)

霍夫代數（Hopf algebras）與從理論物理到計算機科學等多個領域有著廣泛的聯繫，為學生提供了抽象數學應用的瞥見。本書獨特之處在於使這一引人入勝的主題對於高年級本科生和初學研究生變得易於理解。在提供了自成體系的群論和環論介紹後，本書徹底探討了環的譜（spectrum）和扎里斯基拓撲（Zariski topology）的概念。這樣，學生能夠順利地從基本的抽象代數過渡到霍夫代數。霍夫序（Hopf orders）的重要性通過對代數數論、伽羅瓦模理論（Galois module theory）和形式群理論的應用得到了強調。在書籍結束時，讀者將熟悉該領域的既定結果，並準備提出自己的研究問題。

作者簡介

Robert G. Underwood is an Associate Professor of Mathematics at Auburn University. His research interests include the classification of Hopf algebra orders in group rings and the application of Hopf orders to Galois module theory. Professor Underwood earned his PhD in Mathematics in 1992 from the State University of New York at Albany, and his Masters in Math Education in 1986, also from SUNY Albany.

作者簡介(中文翻譯)

羅伯特·G·安德伍德（Robert G. Underwood）是奧本大學（Auburn University）數學系的副教授。他的研究興趣包括群環中霍普代數（Hopf algebra）序的分類，以及霍普序在伽羅瓦模理論（Galois module theory）中的應用。安德伍德教授於1992年在紐約州立大學阿爾巴尼分校（State University of New York at Albany）獲得數學博士學位，並於1986年同樣在SUNY阿爾巴尼獲得數學教育碩士學位。

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