English

Implicit structure in 2-representations of quantum groups

Quantum Algebra 2015-02-24 v3 Representation Theory

Abstract

Given a strong 2-representation of a Kac-Moody Lie algebra (in the sense of Rouquier) we show how to extend it to a 2-representation of categorified quantum groups (in the sense of Khovanov-Lauda). This involves checking certain extra 2-relations which are explicit in the definition by Khovanov-Lauda and, as it turns out, implicit in Rouquier's definition. Some applications are also discussed.

Keywords

Cite

@article{arxiv.1111.1431,
  title  = {Implicit structure in 2-representations of quantum groups},
  author = {Sabin Cautis and Aaron D. Lauda},
  journal= {arXiv preprint arXiv:1111.1431},
  year   = {2015}
}

Comments

33 pages, xypic diagrams; v2 corrects typos in section 7; v3 final version

R2 v1 2026-06-21T19:31:42.498Z