Quantum gl(1|1) and tangle Floer homology

Alexander P. Ellis; Ina Petkova; Vera Vértesi

doi:10.1016/j.aim.2019.04.023

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arXiv · 1510.03483

Quantum gl(1|1) and tangle Floer homology

Alexander P. Ellis·Ina Petkova·Vera Vértesi

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Abstract

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

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Alexander P. Ellis, Ina Petkova, Vera Vértesi. 2015-10-12. Quantum gl(1|1) and tangle Floer homology. https://doi.org/10.1016/j.aim.2019.04.023

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