Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors

By C. Stroppel. 2005

152 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ca54babbd37aa41e1a7e7ab21211c3e7ea26c423

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In Geometry and Topology

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Citations in the corpus

Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “More generally, for link homology theories associated with fundamental sln representations, Webster describes an isomorphism relating his construction to Sussan’s category O based link homology theory [69] , which is related via Koszul duality to a theory defined by Mazorchuk and Stroppel [56].”
Higher Dimensional Algebra VII: Groupoidification (2009, unknown): “Also important were Khovanov’s categorification of the Jones polynomial [25] and the work by Bernstein, Frenkel, Khovanov and Stroppel on categorifying Temperley–Lieb algebras, which are quotients of the type A Hecke algebras [7, 38].”
Category O and slk link invariants (2007, methodology): “This follows from theorem 6.2 of [ Str2 ] except for the base case in the induction hypothesis of proposition 6.4.”
A categorification of quantum sl(n) (2008, methodology): “The symmetric powers V ⊗n 1 of the fundamental representation V1 of U(sl2) were categorified by BFK [7] and extended to the graded case of Uq(sl2) by Stroppel [42].”
A combinatorial approach to functorial quantum slk knot invariants (2007, background): “Our results here are a generalisation of [28], where the case of the Jones polynomial, i.”
Braid cobordisms, triangulated categories, and flag varieties (2006, background): “4. An invariant of tangle cobordisms via highest weight categories was constructed by Stroppel [ St1 , St2], following conjectures in [BFK].”
A categorification of finite-dimensional irreducible representations of quantum $${\mathfrak{sl}_2}$$ and their tensor products (2007, methodology): “So far, invariants of link cobordisms were obtained via a categorification of the Jones polynomial in [Jac04] and [Kho06], [ Str05 ], [Str06].”