Introduction to Cluster Algebras Chapters 1–3
نویسندگان
چکیده
Preface This is a preliminary draft of Chapters 1–3 of our forthcoming textbook Introduction to cluster algebras, joint with Andrei Zelevinsky (1953–2013). We expect to post additional chapters in the not so distant future. This book grew from the ten lectures given by Andrei at the NSF CBMS conference on Cluster Algebras and Applications at North Carolina State University in June 2006. The material of his lectures is much expanded but we still follow the original plan aimed at giving an accessible introduction to the subject for a general mathematical audience. Since its inception in [24], the theory of cluster algebras has been actively developed in many directions. We do not attempt to give a comprehensive treatment of the many connections and applications of this young theory. Our choice of topics reflects our personal taste; much of the book is based on the work done by Andrei and ourselves. Comments and suggestions are welcome.
منابع مشابه
1 2 M ar 2 00 3 CLUSTER ALGEBRAS II : FINITE TYPE CLASSIFICATION
Contents 1. Introduction and main results 2 1.1. Introduction 2 1.2. Basic definitions 3 1.3. Finite type classification 5 1.4. Cluster variables in the finite type 6 1.5. Cluster complexes 7 1.6. Organization of the paper 8 2. Cluster algebras via pseudomanifolds 8 2.1. Pseudomanifolds and geodesic loops 8 2.2. Sufficient conditions for finite type 10 3.
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