The critical CoHA of a quiver with potential

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Abstract

Pursuing the similarity between the Kontsevich--Soibelman construction of the cohomological Hall algebra of BPS states and Lusztig's construction of canonical bases for quantum enveloping algebras, and the similarity between the inetgrality conjecture for motivic Donaldson--Thomas invariants and the PBW theorem for quantum enveloping algebras, we build a coproduct on the cohomological Hall algebra associated to a quiver with potential. We also prove a cohomological dimensional reduction theorem, further linking a special class of cohomological Hall algebras with Yangians, and explaining how to connect the study of character varieties with the study of cohomological Hall algebras.
Original languageEnglish
Pages (from-to)635-703
JournalQuarterly Journal of Mathematics
Volume68
Issue number2
Early online date6 Feb 2017
DOIs
Publication statusPublished - 1 Jun 2017

Keywords

  • math.AG
  • hep-th
  • math.RT

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