On the definition of Kac–Moody 2-category

  title={On the definition of Kac–Moody 2-category},
  author={Jonathan Brundan},
  journal={Mathematische Annalen},
  • 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. 

Super Kac–Moody 2‐categories

We introduce generalizations of Kac–Moody 2‐categories in which the quiver Hecke algebras of Khovanov, Lauda and Rouquier are replaced by the quiver Hecke superalgebras of Kang, Kashiwara and

Categorical actions and crystals

This is an expository article developing some aspects of the theory of categorical actions of Kac-Moody algebras in the spirit of works of Chuang-Rouquier, Khovanov-Lauda, Webster, and many others.

Categorification of the internal braid group action for quantum groups I: 2-functoriality

. We define 2-functors on the categorified quantum group of a simply-laced Kac-Moody algebra that induce Lusztig’s internal braid group action at the level of the Grothendieck group.

On the definition of Heisenberg category

We revisit the definition of the Heisenberg category of central charge k. For central charge -1, this category was introduced originally by Khovanov, but with some additional cyclicity relations

p-DG cyclotomic nilHecke algebras

We categorify a tensor product of two Weyl modules for quantum sl(2) at a prime root of unity.

Monoidal Supercategories

This work is a companion to our article “Super Kac–Moody 2-categories,” which introduces super analogs of the Kac–Moody 2-categories of Khovanov–Lauda and Rouquier. In the case of

The trascendence of Kac-Moody algebras

With the main objective that it can be consulted by all researchers, mainly young people, interested in the study of the Kac-Moody algebras and their applications, this paper aims to present the

An approach to categorification of Verma modules

We give a geometric categorification of the Verma modules M(λ) for quantum sl2 .

p-DG cyclotomic nilHecke algebras II

We categorify tensor products of the fundamental representation of quantum sl2 at prime roots of unity building upon earlier work where a tensor product of two Weyl modules was categorified.



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