Given the monster group, I have no idea what it means to take a power series expansion in this group, I just made up this expression and have been trying to give it a meaningful definition. My main question is whether or not this is a good idea or a bad idea. I will provide some more details.
Let's say the size of the monster group is $M$ then I am thinking about the general linear group of dimension $M$, $GL_M(\mathbb{R})$ and doing matrix power series, then investigating the lie algebra of this type of system. But what I really want is not the entire general linear group, but just the subset corresponding to the representations of the monster group
ok so now I have all the representations of the monster group and am doing formal power series operations on them, is this useful for anything?
Thanks!