I won’t get around to substantive blog posts for at least a few more days, so here is a puzzle.
We usually thinks of groups that occur in nature as permutations of a set which preserve some structure on that set. For example, the general linear group preserves the structure of being an -vector space of dimension .
What structure does the special linear group preserve?
(I have an answer, but I’m curious if it can be stated in a more elementary way.)