Remarks on higher Schwarzians

The Schwarzian derivative has recently received renewed attention in connection with the study of Sachdev–Ye–Kitaev model. In mathematics literature, various higher order generalizations are known due to Aharonov, Bertilsson, and Schippers. Physical applications derivatives have not yet been discussed any detail. this work, we link Bertilsson's variant ℓ–conformal Galilei group, as well discuss some its interesting peculiarities. These include a recurrence relation, which allows one construct Schwarzians iteratively, composition law, symmetry transformations.