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

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2025年1月4日

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R. Jayakumar,
Vijay Kodiyalam

摘要

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 $M^k$ $M^{k}$ of von Neumann algebras. Further, when P is the planar algebra of a finite group, we employ free probability techniques to explicitly identify $M^1$ $M^{1}$ and $M^2$ $M^{2}$ as interpolated free group factors.