Symmetries of the Continuous and Discrete Krichever–Novikov Equation

A symmetry classification is performed for a class of differential-difference equations depending on $9$ parameters. A $6$-parameter subclass of these equations is an integrable discretization of the Krichever–Novikov equation. The dimension $n$ of the Lie point symmetry algebra satisfies $1\le n\le 5$. The highest dimensions, namely $n=5$ and $n=4$ occur only in the integrable cases.