A new proof and a unified version of some well-known formulas of Lie group theory (Q2776284)

The author uses the possibility of embedding any Lie group as a submanifold of some finite dimensional vector space. The goal of his paper is a new coordinate-free proof of some well-known formulas of Lie group theory and a unified version of these formulas. Main result: For each \(n\geq 2\) we have NEWLINE\[NEWLINE\exp(u_1)\cdot \exp(u_2)\dots \exp(u_n)=\exp(\sum_{1\leq i\leq n}u_i+ \sum_{i<j} [u_i,u_j])+ O(r^3),NEWLINE\]NEWLINE where \(r=\max \|u_i\|\).NEWLINENEWLINEFor the entire collection see [Zbl 0978.00017].