Table 3 Commutator table of the Lie algebra of Eq. (3.32)
| Â | \(\varvec{v}^1_1\) | \(\varvec{v}^2_1\) |
|---|---|---|
\(\varvec{v}^1_1\) | 0 | \(\beta \varvec{v}^1_1+\varvec{v}^2_1\) |
\(\varvec{v}^2_1\) | \(-\beta \varvec{v}^1_1-\varvec{v}^2_1\) | 0 |
| Â | \(\varvec{v}^1_1\) | \(\varvec{v}^2_1\) |
|---|---|---|
\(\varvec{v}^1_1\) | 0 | \(\beta \varvec{v}^1_1+\varvec{v}^2_1\) |
\(\varvec{v}^2_1\) | \(-\beta \varvec{v}^1_1-\varvec{v}^2_1\) | 0 |