An Exceptional Collection For Khovanov Homology

Abstract

The Temperley-Lieb algebra is a fundamental component of SU(2) topological quantum field theories. We construct chain complexes corresponding to minimal idempotents in the Temperley-Lieb algebra. Our results apply to the framework which determines Khovanov homology. Consequences of our work include semi-orthogonal decompositions of categorifications of Temperley-Lieb algebras and Postnikov decompositions of all Khovanov tangle invariants.

References in corpus (4)

• Knot invariants and higher representation theory
• Torus knots and the rational DAHA
• Clasp technology to knot homology via the affine Grassmannian
• A categorification of the stable SU(2) Witten-Reshetikhin-Turaev invariant of links in S2 x S1

Cited by in corpus (5)

• Cellular structures using ${\text{U}}_q$-tilting modules
• On stable sl3-homology of torus knots
• Khovanov homology for links in ${\#}^r(S^2\times S^1)$
• Constructing categorical idempotents
• Some Categorical Representations of the Modular Group