Let $A$ be a quantum $\mathbb{P}^n$ defined by $$ A=\mathbb{C}\langle x_1,x_2,\dots,x_{n+1}\rangle/(x_ix_j-r_{ij}x_jx_i)_{1\le i < j\le n+1}. $$ I would like to know the set $X$ of isomorphism classes of point modules for $A$. Here a point module is a cyclic graded right $A$-module $M$ such that each graded piece of $M$ is one-dimensional.

The set $Y$ of isomorphism classes of of point modules for the quantum $\mathbb{P}^2$ $$ \mathbb{C}\langle x_1,x_2,x_3\rangle/(x_ix_j-r_{ij}x_jx_i)_{1\le i < j\le 3} $$ is known to be $\mathbb{P}^2$ or a union of three lines in $\mathbb{P}^2$.

It seems known that $X$ is projective for $n=4$, but does anyone know explicit description of $X$? I tried to compute $X$ in a similar manner as the quantum $\mathbb{P}^2$ case, but it seems quite complicated. I would also appreciate it if someone give me a good description for higher dimensional $n$ case (especially $n=3,4$).

Thank you very much.

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