
Lecture Notes on Cluster Algebras
Robert J. Marsh(Author)
EMS Press
1st Edition
Published in January 2014
Book
Paperback/Softback
122 pages
978-3-03719-130-9 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Zürich
Switzerland
Target group
College/higher education
Graduate students, researchers
Dimensions
Height: 24 cm
Width: 17 cm
ISBN-13
978-3-03719-130-9 (9783037191309)
DOI
10.4171/130
Schweitzer Classification