Abstract
We consider the fermionic -operator based on Bazhanov-Stroganov's three-parameter elliptic parametrization of the free fermion model, and find the most general solution of the related tetrahedral Zamolodchikov algebra in the trigonometric limit for an arbitrary set of parameters. This allows to construct an extension of the -operator and the corresponding Yang-Baxter equation, which are of the difference type in one of the spectral parameters.
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