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This article is available for purchase or by subscription. See below.
Abstract
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We construct a supercategory that can be seen as a skew version of (thickened) KLR algebras
for the type
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
of
level 2.
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Keywords
odd Khovanov homology, categorification, higher
representation theory, KLR algebras
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Mathematical Subject Classification 2010
Primary: 81R50
Secondary: 17B37, 18G60, 57M25
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Milestones
Received: 16 December 2019
Accepted: 8 May 2020
Published: 3 December 2020
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