Lecture Notes on Cluster Algebras (Zurich Lectures in Advanced Mathematics) - Softcover

Robert Marsh

Softcover

ISBN 10: 3037191309 ISBN 13: 9783037191309

Publisher: European Mathematical Society, 2014

Synopsis

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.

Edition details

• Publisher: European Mathematical Society
• Publication date: 2014
• ISBN 10: 3037191309
• ISBN 13: 9783037191309
• Binding: Paperback
• Language: English
• Number of pages: 122