A 2-categorical extension of Etingof–Kazhdan quantisation

Valerio Toledano Laredo, Andrea Appel

Research output: Contribution to journalArticlepeer-review


Let k be a field of characteristic zero. Etingof and Kazhdan (Sel. Math. (N.S.) 2:1–41, 1996) construct a quantisation Ub of any Lie bialgebra b over k, which depends on the choice of an associator Φ. They prove moreover that this quantisation is functorial in b (Etingof and Kazhdan in Sel. Math. (N.S.) 4:213–231, 1998). Remarkably, the quantum group Ub is endowed with a Tannakian equivalence Fb from the braided tensor category of Drinfeld–Yetter modules over b, with deformed associativity constraints given by Φ, to that of Drinfeld–Yetter modules over Ub (Etingof and Kazhdan in Transform. Groups 13:527–539, 2008). In this paper, we prove that the equivalence Fb is functorial in b.
Original languageEnglish
Pages (from-to)3529-3617
Number of pages89
JournalSelecta Mathematica (New Series)
Issue number4
Early online date11 Jan 2018
Publication statusPublished - Sep 2018

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