Knot Invariants and Higher Representation Theory. (Record no. 136199)
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| 000 -LEADER | |
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| fixed length control field | 04326nam a22004573i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC5291691 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131755.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2018 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470442064 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470426507 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5291691 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5291691 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11512050 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1024280888 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA612.2 .W437 2017 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 514.2242 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Webster, Ben. |
| 245 10 - TITLE STATEMENT | |
| Title | Knot Invariants and Higher Representation Theory. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2018. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2017. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (154 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society ; |
| Volume/sequential designation | v.250 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 categorifications -- Chapter 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 structure -- 3. Coevaluation and quantum trace in general -- Chapter 8. Knot invariants -- 1. Constructing knot and tangle invariants -- 2. The unknot for \fg= ₂ -- 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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}_n. The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is \mathfrak{sl}_n, the author shows that these categories agree with certain subcategories of parabolic category \mathcal{O} for \mathfrak{gl}_k. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Knot theory. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Webster, Ben |
| Title | Knot Invariants and Higher Representation Theory |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2018 |
| International Standard Book Number | 9781470426507 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5291691">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5291691</a> |
| Public note | Click to View |
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