# Lie Semigroups?

Why is a Lie group wanted instead of a semigroup, what does the group structure give? References on this would be much appreciated.

I'm currently pondering manifolds and lie groups and their associations with certain computer vision problems. Semigroups or other algebraic objects may be an interesting idea to study in this venture and I wanted to know whether or not a Lie Semigroup is a structure that makes sense to study.

Much of the literature on the representation theory of the group $GL_n$ is really about the representation theory of the monoid $M_n$. (One might argue that it's really about the representation theory of the category Vec.)