On a two-sided Guionnet–Jones–Shlyakhtenko construction and interpolated free group factors arising from finite groups

We formulate a two-sided Guionnet–Jones–Shlyakhtenko-like construction for a subfactor planar algebra P to define two sequences of tracial, unital associative algebras which we show are isomorphic and on completing which, we obtain a sequence M k of von Neumann algebras. Further, when P is the planar algebra of a finite group, we employ free probability techniques to explicitly identify M 1 and M 2 as interpolated free group factors.