Direct Limits of Infinite-Dimensional Lie Groups

Abstract

Many infinite-dimensional Lie groups G of interest can be expressed as the union G = ∪n∈ℕ G n of an ascending sequence \(G_{1} \subseteq G_{2} \subseteq \cdots \) of (finite- or infinite-dimensional) Lie groups. In this survey article, we compile general results concerning such ascending unions, describe the main classes of examples and explain what the general theory tells us about them.