Gauge Structure of Teleparallel Gravity

During the conference "Teleparallel Universes in Salamanca", we became aware of a recent paper [M. Fontanini, E. Huguet, and M. Le Delliou, Phys. Rev. D 99 (2019) 064006] in which some criticisms on the interpretation of teleparallel gravity as a gauge theory for the translation group were put forward. This triggered a discussion about the arguments on which those criticisms were based, whose output is described in the present paper. The main conclusion is that, to a great extent, those arguments are incorrect, and lack mathematical and physical support.