An odd categorification of quantum sl(2)

Abstract

We define a 2-category that categorifies the covering Kac-Moody algebra for sl(2) introduced by Clark and Wang. This categorification forms the structure of a super-2-category as formulated by Kang, Kashiwara, and Oh. The super-2-category structure introduces a (Z x Z_2)-grading giving its Grothendieck group the structure of a free module over the group algebra of Z x Z_2. By specializing the Z_2-action to +1 or to -1, the construction specializes to an "odd" categorification of sl(2) and to a supercategorification of osp(1|2), respectively.

64 pages, tikz diagrams. v2 corrects typos

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• Isotypic faithful $2$-representations of $\mathcal{J}$-simple fiat $2$-categories
• Quantum osp(1|2n) knot invariants are the same as quantum so(2n+1) knot invariants
• DG structures on odd categorified quantum sl(2)
• Canonical bases for the quantum enveloping algebra of gl(m|1) and its modules
• Quantum supergroups VI. Roots of $1$
• Supersymmetric monoidal categories
• Higher Representation Theory and Quantum Affine Schur-Weyl Duality
• Not even Khovanov homology
• Quantum supergroups IV. The modified form
• A geometric setting for quantum osp(1|2)