The elliptic Hall algebra and the deformed Khovanov Heisenberg category

@article{Cautis2018TheEH,
  title={The elliptic Hall algebra and the deformed Khovanov Heisenberg category},
  author={Sabin Cautis and Aaron D. Lauda and Anthony Licata and Peter Samuelson and Joshua Sussan},
  journal={Selecta Mathematica},
  year={2018},
  volume={24},
  pages={4041-4103}
}
We give an explicit description of the trace, or Hochschild homology, of the quantum Heisenberg category defined in  Licata and Savage (Quantum Topol 4(2):125–185, 2013. arXiv:1009.3295). We also show that as an algebra, it is isomorphic to “half” of a central extension of the elliptic Hall algebra of Burban and Schiffmann (Duke Math J 161(7):1171–1231, 2012. arXiv:math/0505148), specialized at $$\sigma = {\bar{\sigma }}^{-1} = q$$σ=σ¯-1=q. A key step in the proof may be of independent interest… 
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