JournalsdmVol. 27pp. 1225–1273

Categorification of the elliptic Hall algebra

  • Youssef Mousaaid

    Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada

  • Alistair Savage

    Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada
Categorification of the elliptic Hall algebra cover
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Abstract

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. 1225–1273

DOI 10.4171/DM/896