Table 1 Table of Lie brackets
\([X_{i},X_{j}]\) | \(X_{1}\) | \(X_{2}\) | \(X_{3}\) | \(X_{4}\) | \(X_{5}\) |
|---|---|---|---|---|---|
\(X_{1}\) | 0 | \(-X_{2}\) | \(-\frac{1}{3}X_{3}\) | 0 | 0 |
\(X_{2}\) | \(X_{2}\) | 0 | 0 | 0 | 0 |
\(X_{3}\) | \(\frac{1}{3}X_{3}\) | 0 | 0 | 0 | 0 |
\(X_{4}\) | 0 | 0 | 0 | 0 | \(-X_{5}\) |
\(X_{5}\) | 0 | 0 | 0 | \(X_{5}\) | 0 |