Buch, Englisch, 122 Seiten, PB, Format (B × H): 170 mm x 240 mm
Buch, Englisch, 122 Seiten, PB, Format (B × H): 170 mm x 240 mm
Reihe: Zurich Lectures in Advanced Mathematics
ISBN: 978-3-03719-130-9
Verlag: EMS Press
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.
Zielgruppe
Graduate students, researchers
