Abstract
An inclusion of II 1 factors N⊂M of finite index has as an invariant, a double sequence of finite-dimensional algebras known as the standard invariant. Planar algebras were introduced by V. Jones as a geometric tool for computing standard invariants of existing subfactors as well as generating standard invariants for new subfactors. In this paper we define a class of planar algebras, termed exchange relation planar algebras, that provides a general framework for understanding several classes of known subfactor inclusions: the Fuss–Catalan algebras (i.e. those coming from the presence of intermediate subfactors) and all depth 2 subfactors. In addition, we present a new class of planar algebras (and thus a new class of subfactors) coming from automorphism subgroups of finite groups.
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Landau, Z.A. Exchange Relation Planar Algebras. Geometriae Dedicata 95, 183–214 (2002). https://doi.org/10.1023/A:1021296230310
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DOI: https://doi.org/10.1023/A:1021296230310