  Some extensions to the Standard Model lead to the introduction of Lorentz
symmetry breaking terms, expected to induce deviations from Lorentz symmetry
around the Planck scale. A parameterization of effects due to Lorentz
invariance violation (LIV) can be introduced by adding an effective term to the
photon dispersion relation. This affects the kinematics of electron-positron
pair creation by TeV $\gamma$ rays on the extragalactic background light (EBL)
and translates into modifications of the standard EBL opacity for the TeV
photon spectra of extragalactic sources. Exclusion limits are presented,
obtained with the spectral analysis of H.E.S.S. observations taken on the
blazar Mrk 501 during the exceptional 2014 flare. The energy spectrum,
extending very significantly above 10 TeV, allows to place strong limits on LIV
in the photon sector at the level of the Planck energy scale for linear
perturbations in the photon dispersion relation, and provides the strongest
constraints presently for the case of quadratic perturbations.
