Lie Group Decompositions and Control
Consider a Lie algebra L and the corresponding connected Lie group eL. A decomposition of eL is a representation of all the elements X of eL as products
X = XrXr−1 · · ·X1, (5.1)
with Xj ∈ Gj , j = 1, ..., r, and Gj are proper subsets of eL. These subsets typically have some further algebraic or geometric structure; for example they are Lie subgroups of eL.