Cohomological Hall algebras and affine quantum groups

• Yaping Yang ^[1] ; Gufang Zhao ^[2]
  1. [1] University of Melbourne

     University of Melbourne

     Australia

     
  2. [2] University of Massachusetts
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 2, 2018, págs. 1093-1119
• Idioma: inglés
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• Resumen

  • We study the preprojective cohomological Hall algebra (CoHA) introduced by the authors in Yang and Zhao (The cohomological Hall algebra of a preprojective algebra. arXiv: 1407.7994v5, 2015) for any quiver Q and any one-parameter formal group G . In this paper, we construct a comultiplication on the CoHA, making it a bialgebra. We also construct the Drinfeld double of the CoHA. The Drinfeld double is a quantum affine algebra of the Lie algebra gQ associated to Q, whose quantization comes from the formal group G . We prove, when the group G is the additive group, the Drinfeld double of the CoHA is isomorphic to the Yangian.