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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 (arXiv link), 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! :)

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    $\begingroup$ That is the Lie algebra, i.e., the tangent space at identity of the algebraic group $E \mod \mu$ over $A/\mu$. $\endgroup$
    – S. Carnahan ♦
    Commented Jul 3, 2019 at 15:20
  • $\begingroup$ Ah! So one considers the endomorphisms, which are a quaternion algebra, as a subgroup of $GL_2$ and then computes the Lie algebra there. Makes sense! Thanks~ :) $\endgroup$
    – Laarz
    Commented Jul 3, 2019 at 15:35

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