#### Volume 15, issue 5 (2015)

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An exceptional collection for Khovanov homology

### Benjamin Cooper and Matt Hogancamp

Algebraic & Geometric Topology 15 (2015) 2659–2706
##### Abstract

The Temperley–Lieb algebra is a fundamental component of $SU\left(2\right)$ 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.

##### Keywords
Jones–Wenzl projector, Temperley–Lieb, categorification
Primary: 57R56
Secondary: 57M27