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Knot Invariants and Higher Representation Theory.
The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for \mathfrak{sl}_2 and \mathfrak{sl}_3 and by Mazorchuk-Stroppel and Sussan for \mathfrak{sl}...
| Call Number: | Libro Electrónico |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Providence :
American Mathematical Society,
2018.
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| Series: | Memoirs of the American Mathematical Society.
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| Subjects: | |
| Online Access: | Texto completo |
Table of Contents:
- Cover; Title page; Chapter 1. Introduction; 1. Quantum topology; 2. Categorification of tensor products; 3. Topology; 4. Summary; Notation; Acknowledgments; Chapter 2. Categorification of quantum groups; 1. Khovanov-Lauda diagrams; 2. The 2-category; 3. A spanning set; 4. Bubble slides; Chapter 3. Cyclotomic quotients; 1. A first approach to the categorification of simples; 2. Categorifications for minimal parabolics; 2.1. The parabolic categorification; 2.2. The quiver flag category; 2.3. The action; 3. Cyclotomic quotients; 4. The categorical action on cyclotomic quotients.
- 5. Universal categorificationsChapter 4. The tensor product algebras; 1. Stendhal diagrams; 2. Definition and basic properties; 3. A basis and spanning set; 4. Splitting red strands; 5. The double tensor product algebras; 6. A Morita equivalence; 7. Decategorification; Chapter 5. Standard modules; 1. Standard modules defined; 2. Simple modules and crystals; 3. Stringy triples; 4. Standard stratification; 5. Self-dual projectives; Chapter 6. Braiding functors; 1. Braiding; 2. Serre functors; Chapter 7. Rigidity structures; 1. Coevaluation and evaluation for a pair of representations.
- 2. Ribbon structure3. Coevaluation and quantum trace in general; Chapter 8. Knot invariants; 1. Constructing knot and tangle invariants; 2. The unknot for \fg= â#x82;#x82;; 3. Independence of projection; 4. Functoriality; Chapter 9. Comparison to category and other knot homologies; 1. Cyclotomic degenerate Hecke algebras; 2. Comparison of categories; 3. The affine case; 4. Comparison to other knot homologies; Bibliography; Back Cover.