DG structures on odd categorified quantum sl(2)

Abstract

We equip Ellis and Brundan's version of the odd categorified quantum group for sl(2) with a differential giving it the structure of a graded dg-2-supercategory. The presence of the super grading gives rise to two possible decategorifications of the associated dg-2-category. One version gives rise to a categorification of quantum sl(2) at a fourth root of unity, while the other version produces a subalgebra of quantum gl(1|1) defined over the integers. Both of these algebras appear in connection with quantum algebraic approaches to the Alexander polynomial.

45 pages with xypic diagrams; v2 corrects typos and modifies discussion of (Q,Pi)-completion

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Cited by in corpus (4)

• p-DG cyclotomic nilHecke algebras
• Quantum supergroups VI. Roots of $1$
• p-DG cyclotomic nilHecke algebras II
• Canonical bases arising from $ı$quantum covering groups