Dimer models and Calabi-Yau algebras / / Nathan Broomhead

• Record Nr.: UNINA9910480937503321
• Autore: Broomhead Nathan <1982->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2011; ©2011
• ISBN: 0-8218-8514-6
• Descrizione fisica: 1 online resource (86 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 215, Number 1011
• Disciplina: 516.3/52
• Soggetti: Toric varieties; Calabi-Yau manifolds; Noncommutative algebras; Geometry, Algebraic; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 215, Number 1011 (second of 5 numbers)."; "January 2012, Volume 215, Number 1011 (second of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""1.1. Overview""; ""1.2. Structure of the article and main results""; ""1.3. Related results""; ""Chapter 2. Introduction to the dimer model""; ""2.1. Quivers and algebras from dimer models""; ""2.2. Symmetries""; ""2.3. Perfect matchings""; ""Chapter 3. Consistency""; ""3.1. A further condition on the R-symmetry""; ""3.2. Rhombus tilings""; ""3.3. Zig-zag flows""; ""3.4. Constructing dimer models""; ""3.5. Some consequences of geometric consistency""; ""Chapter 4. Zig-zag flows and perfect matchings""; ""4.1. Boundary flows""; ""4.2. Some properties of zig-zag flows""""4.3. Right and left hand sides""; ""4.4. Zig-zag fans""; ""4.5. Constructing some perfect matchings""; ""4.6. The extremal perfect matchings""; ""4.7. The external perfect matchings""; ""Chapter 5. Toric algebras and algebraic consistency""; ""5.1. Toric algebras""; ""5.2. Some examples""; ""5.3. Some properties of toric algebras""; ""5.4. Algebraic consistency for dimer models""; ""5.5. Example""; ""Chapter 6. Geometric consistency implies algebraic consistency""; ""6.1. Flows which pass between two ; vertices""; ""6.2. Proof of Proposition 6.2""; ""6.3. Proof of Theorem 6.1""""Chapter 7. Calabi-Yau algebras from algebraically consistent dimers""; ""7.1. Calabi-Yau algebras""; ""7.2. The one sided complex""; ""7.3. Key lemma""; ""7.4. The main result""; ""Chapter 8. Non-commutative crepant resolutions""; ""8.1. Reflexivity""; ""8.2. Non-commutative crepant resolutions""; ""Bibliography""