Vol. 308, No. 1, 2020

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Not even Khovanov homology

Pedro Vaz

Vol. 308 (2020), No. 1, 223–256

We construct a supercategory that can be seen as a skew version of (thickened) KLR algebras for the type A quiver. We use our supercategory to construct homological invariants of tangles and show that for every link our invariant gives a link homology theory supercategorifying the Jones polynomial. Our homology is distinct from even Khovanov homology and we present evidence supporting the conjecture that it is isomorphic to odd Khovanov homology. We also show that cyclotomic quotients of our supercategory give supercategorifications of irreducible finite-dimensional representations of 𝔤𝔩n of level 2.

odd Khovanov homology, categorification, higher representation theory, KLR algebras
Mathematical Subject Classification 2010
Primary: 81R50
Secondary: 17B37, 18G60, 57M25
Received: 16 December 2019
Accepted: 8 May 2020
Published: 3 December 2020
Pedro Vaz
Institut de Recherche en Mathématique et Physique (IRMP)
Université Catholique de Louvain