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On the sharp regularity for arbitrary actions of nilpotent groups on the interval: the case of
In this work, we determine the largest $\unicode[STIX]{x1D6FC}$ for which the nilpotent group of four-by-four triangular matrices with integer coefficients and the value one in the diagonal embeds into the group of $C^{1+\unicode[STIX]{x1D6FC}}$ diffeomorphisms of the closed interval.