Resumen de A 2-categorical extension of Etingof–Kazhdan quantisation

Andrea Appel, Valerio Toledano Laredo

• Let k be a field of characteristic zero. Etingof and Kazhdan (Sel. Math. (N.S.) 2:1–41, 1996) construct a quantisation Uh¯ b of any Lie bialgebra b over k, which depends on the choice of an associator . 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 Uh¯ b is endowed with a Tannakian equivalence Fb from the braided tensor category of Drinfeld–Yetter modules over b, with deformed associativity constraints given by , to that of Drinfeld–Yetter modules over Uh¯ b (Etingof and Kazhdan in Transform. Groups 13:527–539, 2008). In this paper, we prove that the equivalence Fb is functorial in b.