000			04326nam a22004573i 4500
001			EBC5291691
003			MiAaPQ
005			20240729131755.0
006			m o d |
007			cr cnu||||||||
008			240724s2018 xx o ||||0 eng d
020			_a9781470442064 _q(electronic bk.)
020			_z9781470426507
035			_a(MiAaPQ)EBC5291691
035			_a(Au-PeEL)EBL5291691
035			_a(CaPaEBR)ebr11512050
035			_a(OCoLC)1024280888
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA612.2 .W437 2017
082	0		_a514.2242
100	1		_aWebster, Ben.
245	1	0	_aKnot Invariants and Higher Representation Theory.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2018.
264		4	_c©2017.
300			_a1 online resource (154 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.250
505	0		_aCover -- 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			_aThe 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			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic 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	_aKnot theory.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aWebster, Ben _tKnot Invariants and Higher Representation Theory _dProvidence : American Mathematical Society,c2018 _z9781470426507
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5291691 _zClick to View
999			_c136199 _d136199