JournalsqtVol. 11, No. 2pp. 227–294

DG structures on odd categorified quantum sl(2)sl(2)

  • Ilknur Egilmez

    University of Southern California, Los Angeles, USA
  • Aaron D. Lauda

    University of Southern California, Los Angeles, USA
DG structures on odd categorified quantum $sl(2)$ cover

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Abstract

We equip Ellis and Brundan’s version of the odd categorified quantum group for sl(2)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)sl(2) at a fourth root of unity, while the other version produces a subalgebra of quantum gl(11)gl(1|1) defined over the integers. Both of these algebras appear in connection with quantum algebraic approaches to the Alexander polynomial.

Cite this article

Ilknur Egilmez, Aaron D. Lauda, DG structures on odd categorified quantum sl(2)sl(2). Quantum Topol. 11 (2020), no. 2, pp. 227–294

DOI 10.4171/QT/135