Theory and Modern Applications
Table 1 The commutation relations of infinitesimal generators \(\mathcal{X}_{1}\), \(\mathcal{X}_{2}\), \(\mathcal{X}_{3}\)
\([\mathcal{X}_{i},\mathcal{X}_{j}]\) | \(\mathcal{X}_{1}\) | \(\mathcal{X}_{2}\) | \(\mathcal{X}_{3}\) | \(\mathcal{X}_{4}\) |
|---|---|---|---|---|
\(\mathcal{X}_{1}\) | 0 | 0 | 0 | \(-\mathcal{X}_{1}\) |
\(\mathcal{X}_{2}\) | 0 | 0 | 0 | \(\mathcal{X}_{2}\) |
\(\mathcal{X}_{3}\) | 0 | 0 | 0 | \(-3\mathcal{X}_{3}\) |
\(\mathcal{X}_{4}\) | \(\mathcal{X}_{1}\) | \(-\mathcal{X}_{2}\) | \(3\mathcal{X}_{3}\) | 0 |