Table 1 Commutator table
\(\boldsymbol{[X_{i}, X_{j}]}\) | \(\boldsymbol{X_{1}}\) | \(\boldsymbol{X_{2}}\) | \(\boldsymbol{X_{3}}\) |
|---|---|---|---|
\(X_{1}\) | 0 | 0 | \(3X_{1}\) |
\(X_{2}\) | 0 | 0 | \(X_{2}\) |
\(X_{3}\) | \(-3X_{1}\) | \(-X_{2}\) | 0 |
\(\boldsymbol{[X_{i}, X_{j}]}\) | \(\boldsymbol{X_{1}}\) | \(\boldsymbol{X_{2}}\) | \(\boldsymbol{X_{3}}\) |
|---|---|---|---|
\(X_{1}\) | 0 | 0 | \(3X_{1}\) |
\(X_{2}\) | 0 | 0 | \(X_{2}\) |
\(X_{3}\) | \(-3X_{1}\) | \(-X_{2}\) | 0 |