| ($N=2j+1$)\           | $X_2 = \frac{1}{j} \f |
|                       | $[C,V]=V$             | rac{V-V^\dagger}{2\im |
|                       |                       | ath}$,                |
|                       |                       | $X_3 = \frac{1}{j} C$ |
|                       |                       | .                     |
+-----------------------+-----------------------+-----------------------+
| Fuzzy torus           | $C = \sum_{n=0}^{N-1} | $X_1 = \frac{V+V^\dag |
|                       |  C_n |n\rangle \langl | ger}{2}$,             |
|                       | e n|$\                | $X_2 = \frac{V-V^\dag |
|                       | $V=\sum_{n=0}^{N-1} V | ger}{2\imath}$,       |
|                       | _n |n\rangle \langle  | $X_3 = C$.            |
|                       | n+1|$\                |                       |
|                       | with                  |                       |
|                       | $|N\rangle = |0\rangl |                       |
|                       | e$,                   |                       |
|                       | $C_n = \frac{1}{N\alp |                       |
|                       | ha} \sin(\frac{2\pi ( |                       |
|                       | n+\delta)}{N})$       |                       |
|                       | and                   |                       |
|                       | $V_n = \sqrt{\frac{\c |                       |
|                       | os(\frac{2\pi (n+\del |                       |
|                       | ta+0.5)}{N})}{N\alpha |                       |
|                       | \cos(\pi/N)}+\frac{1} |                       |
|                       | {N}}$                 |                       |
|                       | ($\alpha \in \mathbb  |                       |
|                       | R^+$,                 |                       |
|                       | $\delta \in [0,1]$).  |                       |
+-----------------------+-----------------------+-----------------------+
| NC plane              | $\mathfrak{ccr}$      | $X_1 = \frac{a+a^+}{2 |
|                       | algebra               | }$,                   |
|                       | ($N=+\infty$)\        | $X_2 = \frac{a-a^+}{2 |
|                       | $[a,a^+]={\mathrm{id} 