Some authors use $e$ to be the identity element of a group instead of $1$. What is the origin of this notation? Was this before or after we used $e$ to represent the base of the natural logarithm? If after, is there some connection?
We germans (or Kraut, as you might call us) call the identity element "Einheitselement", and hence denote it by $e$ (even though of course not every one does). Similarily it is common to denote a field by $k$ for "Körper"; anyway a great deal of mathematical terminology is of german origin. Likewise the french often denote vector spaces by $E$ ("espace").