Algebraic Operads: An Algorithmic Companion
暫譯: 代數運算子：算法伴侶

Bremner, Murray R., Dotsenko, Vladimir

Algebraic Operads: An Algorithmic Companion
  • 出版商: CRC
  • 出版日期: 2024-10-14
  • 售價: $3,740
  • 貴賓價: 9.5 折 $3,553
  • 語言: 英文
  • 頁數: 384
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 1032921080
  • ISBN-13: 9781032921082
  • 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

Algebraic Operads: An Algorithmic Companion presents a systematic treatment of Gröbner bases in several contexts. The book builds up to the theory of Gröbner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra.

The authors present a variety of topics including: noncommutative Gröbner bases and their applications to the construction of universal enveloping algebras; Gröbner bases for shuffle algebras which can be used to solve questions about combinatorics of permutations; and operadic Gröbner bases, important for applications to algebraic topology, and homological and homotopical algebra.

The last chapters of the book combine classical commutative Gröbner bases with operadic ones to approach some classification problems for operads. Throughout the book, both the mathematical theory and computational methods are emphasized and numerous algorithms, examples, and exercises are provided to clarify and illustrate the concrete meaning of abstract theory.

商品描述(中文翻譯)

《代數運算子：算法伴侶》系統性地探討了在多個背景下的 Gröbner 基底。這本書建立在第二作者與 Khoroshkin 提出的運算子的 Gröbner 基底理論之上，以及相應的鑽石引理在代數中的各種應用。

作者介紹了多種主題，包括：非交換的 Gröbner 基底及其在構建普遍包絡代數中的應用；用於解決排列組合問題的洗牌代數的 Gröbner 基底；以及運算子的 Gröbner 基底，這對於代數拓撲、同調代數和同倫代數的應用非常重要。

本書的最後幾章將經典的交換 Gröbner 基底與運算子的基底結合起來，以解決一些運算子的分類問題。在整本書中，數學理論和計算方法都得到了強調，並提供了大量的算法、範例和練習，以澄清和說明抽象理論的具體意義。

作者簡介

Murray R. Bremner, PhD, is a professor at the University of Saskatchewan in Canada. He attended that university as an undergraduate, and received an M. Comp. Sc. degree at Concordia University in Montréal. He obtained a doctorate in mathematics at Yale University with a thesis entitled On Tensor Products of Modules over the Virasoro Algebra. Prior to returning to Saskatchewan, he held shorter positions at MSRI in Berkeley and at the University of Toronto. Dr. Bremner authored the book Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications and is a co-translator with M. V. Kotchetov of Selected Works of A. I. Shirshov in English Translation. His primary research interests are algebraic operads, nonassociative algebra, representation theory, and computer algebra.

Vladimir Dotsenko, PhD, is an assistant professor in pure mathematics at Trinity College Dublin in Ireland. He studied at the Mathematical High School 57 in Moscow, Independent University of Moscow, and Moscow State University. His PhD thesis is titled Analogues of Orlik-Solomon Algebras and Related Operads. Dr. Dotsenko also held shorter positions at Dublin Institute for Advanced Studies and the University of Luxembourg. His collaboration with Murray started in February 2013 in CIMAT (Guanajuato, Mexico), where they both lectured in the research school "Associative and Nonassociative Algebras and Dialgebras: Theory and Algorithms." His primary research interests are algebraic operads, homotopical algebra, combinatorics, and representation theory.

作者簡介(中文翻譯)

Murray R. Bremner，博士，是加拿大薩斯喀徹溫大學的教授。他在該大學完成本科學位，並在蒙特利爾的康考迪亞大學獲得計算機科學碩士學位。他在耶魯大學獲得數學博士學位，論文題目為On Tensor Products of Modules over the Virasoro Algebra。在回到薩斯喀徹溫之前，他曾在伯克利的數學科學研究所（MSRI）和多倫多大學擔任短期職位。Bremner博士著有書籍Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications，並與M. V. Kotchetov共同翻譯Selected Works of A. I. Shirshov in English Translation。他的主要研究興趣包括代數操作子、非結合代數、表示理論和計算機代數。

Vladimir Dotsenko，博士，是愛爾蘭都柏林三一學院的純數學助理教授。他曾在莫斯科的數學高級中學57、獨立莫斯科大學和莫斯科國立大學學習。他的博士論文題目為Analogues of Orlik-Solomon Algebras and Related Operads。Dotsenko博士也曾在都柏林高級研究所和盧森堡大學擔任短期職位。他與Murray的合作始於2013年2月在CIMAT（墨西哥瓜納華托），他們在研究學校「結合代數與非結合代數及對代數：理論與算法」中共同授課。他的主要研究興趣包括代數操作子、同倫代數、組合數學和表示理論。

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