On the definition of Kac–Moody 2-category

@article{Brundan2015OnTD,
  title={On the definition of Kac–Moody 2-category},
  author={Jonathan Brundan},
  journal={Mathematische Annalen},
  year={2015},
  volume={364},
  pages={353-372}
}
  • J. Brundan
  • Published 2 January 2015
  • Mathematics
  • Mathematische Annalen
We show that the Kac–Moody 2-categories defined by Rouquier and by Khovanov and Lauda are the same. 

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References

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A diagrammatic approach to categorification of quantum groups II

We categorify the idempotented form of quantum sl(n).

Implicit structure in 2-representations of quantum groups

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).

A Categorification of Quantum

In this paper, we categorify the algebra Uq with the same approach as in [A. Lauda, Adv. Math. (2010), arXiv:math.QA/0803.3652; M. Khovanov, Comm. Algebra 11 (2001) 5033]. The algebra U = Uq is

2-Kac-Moody algebras

We construct a 2-category associated with a Kac-Moody algebra and we study its 2-representations. This generalizes earlier work with Chuang for type A. We relate categorifications relying on K_0