03275nam 2200613 450 991078861890332120170822144511.00-8218-9110-3(CKB)3360000000464089(EBL)3114401(SSID)ssj0000888921(PQKBManifestationID)11456893(PQKBTitleCode)TC0000888921(PQKBWorkID)10866997(PQKB)10241592(MiAaPQ)EBC3114401(RPAM)17322715(PPN)195419189(EXLCZ)99336000000046408920150415h20112011 uy 0engur|n|---|||||txtccrExtended graphical calculus for categorified quantum sl(2) /Mikhail Khovano [and three others]Providence, Rhode Island :American Mathematical Society,2011.©20111 online resource (87 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 219, Number 1029"September 2012, Volume 219, Number 1029 (second of 5 numbers)."0-8218-8977-X Includes bibliographical references.""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""1.1. The algebra ""; ""1.2. Categorification""; ""1.3. Diagrammatics for the Karoubi envelope ""; ""1.4. Categorification and symmetric functions""; ""1.5. Relations to other categorifications""; ""Chapter 2. Thick calculus for the nilHecke ring""; ""2.1. The nilHecke ring and its diagrammatics""; ""2.2. Boxes, thick lines, and splitters""; ""2.3. Partitions, symmetric functions, and their diagrammatics""; ""2.4. Splitter equations, explosions, and idempotents""; ""2.5. The nilHecke algebra as a matrix algebra over its center""""Chapter 3. Brief review of calculus for categorified sl(2)""""3.1. The algebra ""; ""3.2. The 2-category ""; ""3.3. Box notation for ""; ""3.4. Karoubi envelope""; ""Chapter 4. Thick calculus and ""; ""4.1. Thick lines oriented up or down""; ""4.2. Splitters as diagrams for the inclusion of a summand""; ""4.3. Adding isotopies via thick caps and cups""; ""4.4. Thin bubble slides""; ""4.5. Thick bubbles""; ""4.6. Thick bubble slides and some key lemmas""; ""Chapter 5. Decompositions of functors and other applications""; ""5.1. Decomposition of â?°^{( )}â?°^{( )}1_{ }""""5.2. Decomposition of â?°^{( )}â?±^{( )}1_{ }""""5.3. Indecomposables over â??""; ""5.4. Bases for HOMs between some 1-morphisms""; ""Bibliography""Memoirs of the American Mathematical Society ;Volume 219, Number 1029.Categories (Mathematics)Quantum groupsSymmetric functionsFinite fields (Algebra)Categories (Mathematics)Quantum groups.Symmetric functions.Finite fields (Algebra)512/.482Khovanov MikhailMiAaPQMiAaPQMiAaPQBOOK9910788618903321Extended graphical calculus for categorified quantum sl(2)3743113UNINA