This might be a silly question, and if it has been asked somewhere else, I would appreciate a link; however, I was unable to find it myself.

In this paper by Lauter-Viray, https://arxiv.org/abs/1206.6942, in the proof of Theorem 1.5 (page 10, near the top) they give definitions for some objects whose elements they wish to count, namely $S_n$ and $S_n^{\text{Lie}}$.

I don't understand the definition of the latter, but moreover, I don't know what is meant by equality in $\text{Lie}(E\bmod \mu).$ What is the Lie group in question? It seems to be a subgroup of the endomorphism ring, but the precise definition is never given.

Any and all help is appreciated.

Thanks in advance! :)