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On the definition of Kac-Moody 2-category. (English) Zbl 1395.17014
The main result of the paper asserts that Rouquier’s Kac-Moody \(2\)-category associated to a symmetrizable generalized Cartan matrix is isomorphic to the corresponding Khovanov and Lauda \(2\)-category (in a more general definition of Cautis and Lauda). The proof is done by an elementary but technically very non-trivial relation chase.

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
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References:
[1] Cautis, S; Lauda, A, Implicit structure in 2-representations of quantum groups, Selecta Math., 21, 201-244, (2015) · Zbl 1370.17017
[2] Khovanov, M; Lauda, A, A diagrammatic approach to categorification of quantum groups III, Quantum Top., 1, 1-92, (2010) · Zbl 1206.17015
[3] Lauda, A, A categorification of quantum \(\mathfrak{sl}(2)\), Adv. Math., 225, 3327-3424, (2010) · Zbl 1219.17012
[4] Rouquier, R.: 2-Kac-Moody algebras. arXiv:0812.5023 · Zbl 1247.20002
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