Abstract
We show that the trace decategorification, or zeroth Hochschild homology, of the twisted Heisenberg category defined by Cautis and Sussan is isomorphic to a quotient of \({W^-}\), a subalgebra of \({W_{1+\infty}}\) defined by Kac, Wang, and Yan. Our result is a twisted analogue of that by Cautis, Lauda, Licata, and Sussan relating \({W_{1+\infty}}\) and the trace decategorification of the Heisenberg category.
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Communicated by Y. Kawahigashi
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Oğuz, C.O., Reeks, M. Trace of the Twisted Heisenberg Category. Commun. Math. Phys. 356, 1117–1154 (2017). https://doi.org/10.1007/s00220-017-2992-9
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DOI: https://doi.org/10.1007/s00220-017-2992-9