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arXiv · 1808.04924

DG structures on odd categorified quantum sl(2)

Aaron D. Lauda·Ilknur Egilmez
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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.

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Aaron D. Lauda, Ilknur Egilmez. 2020-09-10. DG structures on odd categorified quantum sl(2). https://doi.org/10.4171/qt%2F135

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