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Foundations of Garside Theory
 
Patrick Dehornoy University of Caen, France

with François Digne, Eddy Godelle, Daan Krammer, and Jean Michel

A publication of European Mathematical Society
Foundations of Garside Theory
Hardcover ISBN:  978-3-03719-139-2
Product Code:  EMSTM/24
List Price: $119.00
AMS Member Price: $95.20
Please note AMS points can not be used for this product
Foundations of Garside Theory
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Foundations of Garside Theory
Patrick Dehornoy University of Caen, France

with François Digne, Eddy Godelle, Daan Krammer, and Jean Michel

A publication of European Mathematical Society
Hardcover ISBN:  978-3-03719-139-2
Product Code:  EMSTM/24
List Price: $119.00
AMS Member Price: $95.20
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Tracts in Mathematics
    Volume: 242015; 710 pp
    MSC: Primary 20; Secondary 05; 18;

    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.

    Readership

    Undergraduate and graduate students interested in Garside theory.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 242015; 710 pp
MSC: Primary 20; Secondary 05; 18;

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.

Readership

Undergraduate and graduate students interested in Garside theory.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.