Cluster Algebra and Poisson Geometry (Mathematical Surveys and Monographs)

Gekhtman, Michael, Michael Shapiro und Alek Vainshtein:

ISBN 10: 0821849727 / ISBN 13: 9780821849729

Published by American Mathematical Society, 2010

About this Item

246 Seiten; 9780821849729.3 Gewicht in Gramm: 1.

Seller Inventory # 1072138

Bibliographic Details

• Title: Cluster Algebra and Poisson Geometry (Mathematical Surveys and Monographs)
• Publisher: American Mathematical Society
• Publication Date: 2010
• Language: English
• ISBN 10: 0821849727
• ISBN 13: 9780821849729
• Binding: hardcover
• Condition: Gut
• Weight: 1 gram
• Seller catalogs:
  • Varia

About this title

Synopsis

Cluster algebras, introduced by Fomin and Zelevinsky in 2001, are commutative rings with unit and no zero divisors equipped with a distinguished family of generators (cluster variables) grouped in overlapping subsets (clusters) of the same cardinality (the rank of the cluster algebra) connected by exchange relations. Examples of cluster algebras include coordinate rings of many algebraic varieties that play a prominent role in representation theory, invariant theory, the study of total positivity, etc. The theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links to a wide range of subjects including representation theory, discrete dynamical systems, Teichmüller theory, and commutative and non-commutative algebraic geometry. This book is the first devoted to cluster algebras. After presenting the necessary introductory material about Poisson geometry and Schubert varieties in the first two chapters, the authors introduce cluster algebras and prove their main properties in Chapter 3. This chapter can be viewed as a primer on the theory of cluster algebras. In the remaining chapters, the emphasis is made on geometric aspects of the cluster algebra theory, in particular on its relations to Poisson geometry and to the theory of integrable systems.

About the Author

Michael J. Shapiro, professor of political science at the University of Hawai'i, is the author of numerous books, including Methods and Nations: Cultural Governance and the Indigenous Subject.