Parameters in Categorified Quantum Groups

  • Aaron D. LaudaEmail author


In this note we give explicit isomorphisms of 2-categories between various versions of the categorified quantum group associated to a simply-laced Kac-Moody algebra. These isomorphisms are convenient when working with the categorified quantum group. They make it possible to translate results from the \(\mathfrak {g}\mathfrak {l}_{n}\) variant of the 2-category to the \(\mathfrak {s}\mathfrak {l}_{n}\) variant and transfer results between various conventions in the literature. We also extend isomorphisms of finite type KLR algebras for different choices of parameters to the level of 2-categories.


Categorification Quantum group KLR-algebra 


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The author is partially supported by the NSF grants DMS-1255334 and DMS-1664240. He would also like to thank Joshua Sussan and Hoel Queffelec for comments on an early version of this note.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA

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