#### Vol. 308, No. 1, 2020

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Not even Khovanov homology

### Pedro Vaz

Vol. 308 (2020), No. 1, 223–256
##### Abstract

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 ${\mathfrak{𝔤}\mathfrak{𝔩}}_{n}$ of level 2.

##### Keywords
odd Khovanov homology, categorification, higher representation theory, KLR algebras
##### Mathematical Subject Classification 2010
Primary: 81R50
Secondary: 17B37, 18G60, 57M25