DG structures on odd categorified quantum sl(2)
Quantum Algebra
2020-12-03 v2 Representation Theory
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.
Cite
@article{arxiv.1808.04924,
title = {DG structures on odd categorified quantum sl(2)},
author = {Aaron D. Lauda and Ilknur Egilmez},
journal= {arXiv preprint arXiv:1808.04924},
year = {2020}
}
Comments
45 pages with xypic diagrams; v2 corrects typos and modifies discussion of (Q,Pi)-completion