First recall the Jordan-Hölder theorem for groups: > **Theorem** (Jordan-Hölder): Let $G$ be a group, and let $$ G=G_1 \supset G_2 \supset ... \supset G_r = \{ e \} $$ be a normal tower such that each group > $G_i /G_{i+1}$ is simple, and $G_i \neq G_{i+1}$ for $0<i<r$. > Then any other normal tower of $G$ having the same properties is > equivalent to this one (i.e. the sequence of factor groups in our two > towers are the same up to isomorphisms, and a permutation of the > indices). [This paper][1] of Kodiyalam-Landau-Sunder contains the basic definition of a planar algebra, of a group (subfactor) planar algebra, the definitions (p16) of planar algebra morphism, planar ideal and quotient. We note that the planar ideals are precisely the kernel of the planar algebra morphisms ! We call a planar algebra **simple** if it has no non-trivial planar ideal. > **Question 1** : Do the planar ideals of a group planar algebra correspond to the normal subgroups ? If yes, a group planar algebra is simple iff the group is simple. If no, how adapt the concept of planar ideal for having a positive answer ? >**Question 2** : Let $\mathcal{P}$ be a planar algebra, and let $$ \mathcal{P}=\mathcal{J}_1 \supset \mathcal{J}_2 \supset ... \supset \mathcal{J}_r = (0) $$ be an ideal tower such that each quotient > $\mathcal{J}_i /\mathcal{J}_{i+1}$ is simple, and $\mathcal{J}_i \neq \mathcal{J}_{i+1}$ for $0<i<r$. > Then any other ideal tower of $\mathcal{P}$ having the same properties is > equivalent to this one (i.e. the sequence of quotient planar algebras in our two towers are the same up to isomorphisms, and a permutation of the > indices) ? [1]: http://www.imsc.res.in/~sunder/paha.pdf