We show that the central charge reduction of the universal central extension of the elliptic Hall algebra is isomorphic to the trace, or zeroth Hochschild homology, of the quantum Heisenberg category of central charge . As an application, we construct large families of representations of the universal extension of the elliptic Hall algebra.
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Youssef Mousaaid, Alistair Savage, Categorification of the elliptic Hall algebra. Doc. Math. 27 (2022), pp. 1225–1273DOI 10.4171/DM/896