Exchange Relation Planar Algebras |
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Authors: | Zeph A. Landau |
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Affiliation: | (1) Mathematical Sciences Research Institute, 1000 Centenial Drive, # 5070, Berkeley, CA, 94720-5070, U.S.A. |
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Abstract: | An inclusion of II1 factors NM 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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Keywords: | depth two inclusions exchange relation planar algebras Fuss– Catalan algebras operator algebras planar algebras standard invariant subfactors von Neumann algebras |
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