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We identify the Grothendieck group of the tangle Floer dg algebra with atensor product of certain $U_q(gl(1|1))$ representations. Under thisidentification, up to a scalar factor, the map on the Grothendieck groupinduced by the tangle Floer dg bimodule associated to a tangle agrees with theReshetikhin-Turaev homomorphism for that tangle. We also introduce dg bimoduleswhich act on the Grothendieck group as the generators $E$ and $F$ of$U_q(gl(1|1))$.

Quantum gl(1|1) and tangle Floer homology