A 2-categorical extension of Etingof–Kazhdan quantisation

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Abstract

Let \(\mathsf {k}\) be a field of characteristic zero. Etingof and Kazhdan (Sel. Math. (N.S.) 2:1–41, 1996) construct a quantisation \(U_\hbar \mathfrak b\) of any Lie bialgebra \(\mathfrak b\) over \(\mathsf {k}\), which depends on the choice of an associator \(\Phi \). They prove moreover that this quantisation is functorial in \(\mathfrak b\) (Etingof and Kazhdan in Sel. Math. (N.S.) 4:213–231, 1998). Remarkably, the quantum group \(U_\hbar \mathfrak b\) is endowed with a Tannakian equivalence \(F_{\mathfrak b}\) from the braided tensor category of Drinfeld–Yetter modules over \(\mathfrak b\), with deformed associativity constraints given by \(\Phi \), to that of Drinfeld–Yetter modules over \(U_\hbar \mathfrak b\) (Etingof and Kazhdan in Transform. Groups 13:527–539, 2008). In this paper, we prove that the equivalence \(F_{\mathfrak b}\) is functorial in \(\mathfrak b\).

Mathematics Subject Classification

17B37 81R50 17B62 

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsUniversity of EdinburghEdinburghUK
  2. 2.Department of MathematicsNortheastern UniversityBostonUSA

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