LEADER 03478nam 2200625 450 001 9910480937503321 005 20170822144524.0 010 $a0-8218-8514-6 035 $a(CKB)3360000000464071 035 $a(EBL)3114383 035 $a(SSID)ssj0000888889 035 $a(PQKBManifestationID)11492666 035 $a(PQKBTitleCode)TC0000888889 035 $a(PQKBWorkID)10866566 035 $a(PQKB)10972532 035 $a(MiAaPQ)EBC3114383 035 $a(PPN)195419006 035 $a(EXLCZ)993360000000464071 100 $a20150416h20112011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDimer models and Calabi-Yau algebras /$fNathan Broomhead 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2011. 210 4$dİ2011 215 $a1 online resource (86 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 215, Number 1011 300 $a"Volume 215, Number 1011 (second of 5 numbers)." 300 $a"January 2012, Volume 215, Number 1011 (second of 5 numbers)." 311 $a0-8218-5308-2 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""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"" 327 $a""6.3. Proof of Theorem 6.1""""Chapter 7. Calabi-Yau algebras from algebraically consistent dimers""; ""7.1. Calabi-Yau algebras""; ""7.2. The one sided complex""; ""7.3. Key lemma""; ""7.4. The main result""; ""Chapter 8. Non-commutative crepant resolutions""; ""8.1. Reflexivity""; ""8.2. Non-commutative crepant resolutions""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 215, Number 1011. 606 $aToric varieties 606 $aCalabi-Yau manifolds 606 $aNoncommutative algebras 606 $aGeometry, Algebraic 608 $aElectronic books. 615 0$aToric varieties. 615 0$aCalabi-Yau manifolds. 615 0$aNoncommutative algebras. 615 0$aGeometry, Algebraic. 676 $a516.3/52 700 $aBroomhead$b Nathan$f1982-$0919061 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480937503321 996 $aDimer models and Calabi-Yau algebras$92061296 997 $aUNINA