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Lecture Notes on Cluster Algebras

Marsh, Robert J.,

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Lecture Notes on Cluster Algebras

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lecture Notes on Cluster Algebras/ Robert J. Marsh
Author:	Marsh, Robert J.,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2014,
Description:	1 online resource (121 pages)
Subject:	Groups & group theory -
Online resource:	https://doi.org/10.4171/130
Online resource:	https://www.ems-ph.org/img/books/marsh_mini.jpg
ISBN:	9783037196304

Lecture Notes on Cluster Algebras
Marsh, Robert J.,

Lecture Notes on Cluster Algebras[electronic resource] /Robert J. Marsh - Zuerich, Switzerland :European Mathematical Society Publishing House,2014 - 1 online resource (121 pages) - Zurich Lectures in Advanced Mathematics (ZLAM).

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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. The 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.

ISBN: 9783037196304

Standard No.: 10.4171/130doiSubjects--Topical Terms:

3480852
Groups & group theory

Lecture Notes on Cluster Algebras
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