【2015】 Foundations of Garside Theory
Book 图书名称： Foundations of Garside Theory
Author 作者： Patrick Dehornoy
Publisher 出版社： European Mathematical Society
Page 页数： 710
Publishing Date 出版时间： may 31, 2015
Language 语言： English
Size 大小： 7 MB
Format 格式： pdf 文字版
ISBN: 3037191392, 9783037191392
Edition: 第1版 搜索过论坛，没有该文档
This text is a monograph on algebra, with connections to geometry and low-dimensional topology. It mainly involves groups, monoids, and categories, and aims to provide a unified treatment for those situations in which one can find distinguished decompositions by iteratively extracting a maximal fragment lying in a prescribed family. Initiated in 1969 by F. A. Garside in the case of Artin's braid groups, this approach led to interesting results in a number of cases, the central notion being what the authors call a Garside family. The study is far from complete, and the purpose of this book is to present the current state of the theory and to invite further research. The book has two parts: In Part A, the bases of a general theory, including many easy examples, are developed. In Part B, various more sophisticated examples are specifically addressed. To make the content accessible to a wide audience of nonspecialists, the book's exposition is essentially self-contained and very few prerequisites are needed. In particular, it should be easy to use this as a textbook both for Garside theory and for the more specialized topics investigated in Part B: Artin-Tits groups, Deligne-Lusztig varieties, groups of algebraic laws, ordered groups, and structure groups of set-theoretic solutions of the Yang-Baxter equation. The first part of the book can be used as the basis for a graduate or advanced undergraduate course. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
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