A 2-categorical extension of Etingof–Kazhdan quantisation

• Andrea Appel ^[1] ; Valerio Toledano Laredo ^[2]
  1. [1] University of Edinburgh

     University of Edinburgh

     Reino Unido

     
  2. [2] Northeastern University

     Northeastern University

     City of Boston, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 4, 2018, págs. 3529-3617
• Idioma: inglés
• Enlaces
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• Resumen

  • 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.