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Lecture Notes on Cluster Algebras
 
Robert J. Marsh University of Leeds, United Kingdom
A publication of European Mathematical Society
Lecture Notes on Cluster Algebras
Softcover ISBN:  978-3-03719-130-9
Product Code:  EMSZLEC/19
List Price: $36.00
AMS Member Price: $28.80
Please note AMS points can not be used for this product
Lecture Notes on Cluster Algebras
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Lecture Notes on Cluster Algebras
Robert J. Marsh University of Leeds, United Kingdom
A publication of European Mathematical Society
Softcover ISBN:  978-3-03719-130-9
Product Code:  EMSZLEC/19
List Price: $36.00
AMS Member Price: $28.80
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Zurich Lectures in Advanced Mathematics
    Volume: 192014; 122 pp
    MSC: Primary 13; 05; 14; 17; 18; 20; 51; 52; 57;

    Cluster algebras are combinatorially defined commutative algebras which were introduced by S. Fomin and A. Zelevinsky as a tool for studying the dual canonical basis of a quantized enveloping algebra and totally positive matrices. The aim of these notes is to give an introduction to cluster algebras which is accessible to graduate students or researchers interested in learning more about the field while giving a taste of the wide connections between cluster algebras and other areas of mathematics.

    The approach taken emphasizes combinatorial and geometric aspects of cluster algebras. Cluster algebras of finite type are classified by the Dynkin diagrams, so a short introduction to reflection groups is given in order to describe this and the corresponding generalized associahedra. A discussion of cluster algebra periodicity, which has a close relationship with discrete integrable systems, is included.

    This book ends with a description of the cluster algebras of finite mutation type and the cluster structure of the homogeneous coordinate ring of the Grassmannian, both of which have a beautiful description in terms of combinatorial geometry.

    A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

    Readership

    Graduate students and research mathematicians interested in cluster algebras.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 192014; 122 pp
MSC: Primary 13; 05; 14; 17; 18; 20; 51; 52; 57;

Cluster algebras are combinatorially defined commutative algebras which were introduced by S. Fomin and A. Zelevinsky as a tool for studying the dual canonical basis of a quantized enveloping algebra and totally positive matrices. The aim of these notes is to give an introduction to cluster algebras which is accessible to graduate students or researchers interested in learning more about the field while giving a taste of the wide connections between cluster algebras and other areas of mathematics.

The approach taken emphasizes combinatorial and geometric aspects of cluster algebras. Cluster algebras of finite type are classified by the Dynkin diagrams, so a short introduction to reflection groups is given in order to describe this and the corresponding generalized associahedra. A discussion of cluster algebra periodicity, which has a close relationship with discrete integrable systems, is included.

This book ends with a description of the cluster algebras of finite mutation type and the cluster structure of the homogeneous coordinate ring of the Grassmannian, both of which have a beautiful description in terms of combinatorial geometry.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in cluster algebras.

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.