03476nam 2200625 450 991078861690332120170822144524.00-8218-8514-6(CKB)3360000000464071(EBL)3114383(SSID)ssj0000888889(PQKBManifestationID)11492666(PQKBTitleCode)TC0000888889(PQKBWorkID)10866566(PQKB)10972532(MiAaPQ)EBC3114383(RPAM)16990408(PPN)195419006(EXLCZ)99336000000046407120150416h20112011 uy 0engur|n|---|||||txtccrDimer models and Calabi-Yau algebras /Nathan BroomheadProvidence, Rhode Island :American Mathematical Society,2011.©20111 online resource (86 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 215, Number 1011"Volume 215, Number 1011 (second of 5 numbers).""January 2012, Volume 215, Number 1011 (second of 5 numbers)."0-8218-5308-2 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Volume 215, Number 1011.Toric varietiesCalabi-Yau manifoldsNoncommutative algebrasGeometry, AlgebraicToric varieties.Calabi-Yau manifolds.Noncommutative algebras.Geometry, Algebraic.516.3/52Broomhead Nathan1982-1542987MiAaPQMiAaPQMiAaPQBOOK9910788616903321Dimer models and Calabi-Yau algebras3796216UNINA