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Record Nr. |
UNINA9910788618903321 |
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Titolo |
Extended graphical calculus for categorified quantum sl(2) / / Mikhail Khovano [and three others] |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2011 |
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©2011 |
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ISBN |
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Descrizione fisica |
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1 online resource (87 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 219, Number 1029 |
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Disciplina |
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Soggetti |
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Categories (Mathematics) |
Quantum groups |
Symmetric functions |
Finite fields (Algebra) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"September 2012, Volume 219, Number 1029 (second of 5 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""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_{ }"" |
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""5.2. Decomposition of â?°^{( )}â?±^{( )}1_{ }""""5.3. Indecomposables over â??""; ""5.4. Bases for HOMs between some 1-morphisms""; ""Bibliography"" |
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