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出版者:Cambridge University Press

作者:Ross Street

出品人:

页数:260

译者:

出版时间:2007-01-29

价格:USD 58.00

装帧:Paperback

isbn号码:9780521695244

丛书系列:Australian Mathematical Society Lecture Series

图书标签:

数学
量子群
代数
数学
表示论
Hopf代数
量子变形
李代数
拓扑量子场论
可积系统
数学物理

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具体描述

Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn the latest algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.

这本图书《Quantum Groups》深入探讨了量子群这一重要的数学概念，它为读者提供了一种独特且严谨的视角来理解现代代数结构的发展与变革。作者将复杂的理论知识系统地展现出来，力求让每个章节都充满洞见和启发。书中涵盖了从基础概念到高级应用的全面内容，帮助读者不仅掌握核心定义，还能理解其在物理、数学以及其他学科中的深远意义。通过细致入微的解释，这本书详细介绍了量子群的历史背景及其与传统群论的区别。作者用清晰的语言和逻辑严谨的结构，逐步引导读者理解这些抽象概念在数学体系中的地位和作用。同时，本书还包含大量经典问题和开放性讨论，让读者能够深入思考相关领域的发展方向。书中通过丰富的例子和具体案例，使理论更加贴近实际应用，帮助读者建立起对量子群的直观认识。这不仅适合数学专业的学生，还欢迎那些对前沿科学研究感兴趣的读者。无论是从基础学习还是深入研究，这本图书都提供了非常有价值的内容。作者注重将抽象与具体结合，详尽地描绘量子群在现代数学中的重要角色。这不仅展示了该领域的发展脉络，也引导读者理解其潜在的应用前景。在每一节段中，书写都充满了对问题的思考和探索，旨在激发读者的兴趣与学习动力。通过精心设计的结构和详尽的内容，这本图书为读者打开了一扇深入探索数学世界的大门，同时也展现了作者对学科研究的高度重视。无论你是刚接触这个领域的新手，还是有一定基础的学者，本书都将为你提供有价值的资源和指导，帮助你不断拓宽知识边界，提升学术素养。总的来说，这是一本既严谨又富有启发性的著作，能够满足不同读者的学习需求，让他们在阅读过程中获得丰富的思维体验与知识积累。希望这份详细介绍能为你提供一个全面而深入的参考依据。

作者简介

Ross Street is a Professor of Mathematics and Director of the Centre of Australian Category Theory at Macquarie University. He is also a Fellow of the Australian Academy of Science.

目录信息

Introduction
1. Revision of basic structures
2. Duality between geometry and algebra
3. The quantum general linear group
4. Modules and tensor products
5. Cauchy modules
6. Algebras
7. Coalgebras and bialgebras
8. Dual coalgebras of algebras
9. Hopf algebras
10. Representations of quantum groups
11. Tensor categories
12. Internal homs and duals
13. Tensor functors and Yang-Baxter operators
14. A tortile Yang-Baxter operator for each finite-dimensional vector space
15. Monoids in tensor categories
16. Tannaka duality
17. Adjoining an antipode to a bialgebra
18. The quantum general linear group again
19. Solutions to exercises
References
Index
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