DG structures on odd categorified quantum sl(2)

2018/08/31 by Aaron D. Lauda, Ilknur Egilmez · 6 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Categorification #Mathematics #Physics #Pure mathematics #Quantum #Quantum mechanics #math.QA #math.RT #msc:17A70 #msc:17B37 #msc:20G42 #msc:57M27

paper · pdf · doi:10.4171/qt/135

published in Quantum Topology 11(2), 227-294 · 45 pages with xypic diagrams; v2 corrects typos and modifies discussion of (Q,Pi)-completion

openalex created_date 2018/08/22 · openalex publication_date 2020/06/22 · arxiv created 2020/09/10 · arxiv updated 2020/12/03 · openalex updated_date 2026/08/05

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.

Citations

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