# Correction to: Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras

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## Mathematics Subject Classification

81R50 16G 16T25 17B37## 1 Correction to: Invent. math. (2018) 211:591–685 https://doi.org/10.1007/s00222-017-0754-0

*commuting family of central objects*if it satisfies two conditions

- (a)for any \(i\in I\), \(R_{P_i}\) is an isomorphism functorial in \(X\in {\mathcal T}\) such that
- (b)
\(R_{P_j}(P_i)\circ R_{P_i}(P_j)={\text {id}}_{P_i\mathop \otimes P_j}\) for any \(i,j\in I\) such that \(i \ne j\).

*strictly commuting family of central objects*.

The problem occurs since we do not assume that the family satisfy condition (A.4). As the simplest remedy, we include condition (A.4) in the definition of commuting family of central objects from the beginning and remove the definition of strictly commuting family of central objects in the paper. Under the new definition of commuting family of central objects, we can construct the category \({\mathcal T}[P_i^{\mathop \otimes -1} \mid i \in I]\) as well as the category \({\mathcal T}[P_i\simeq \mathbf{{1}}\mid i\in I]\) in the graded case (Appendix A.7). All the arguments in the main body of our paper also work without any problem.

## Notes

## References

- 1.Kang, S.-J., Kashiwara, M., Kim, M.: Symmetric quiver Hecke algebras and \(R\)-matrices of quantum affine algebras. Invent. Math.
**211**, 591–685 (2018)MathSciNetCrossRefzbMATHGoogle Scholar - 2.Kashiwara, M., Schapira, P.: Categories and Sheaves, Grundlehren der mathematischen Wissenschaften 332. Springer, Berlin (2006)Google Scholar