The Planar Algebra of Diagonal Subfactors
نویسنده
چکیده
There is a natural construction which associates to a finitely generated, countable, discrete group G and a 3-cocycle ω of G an inclusion of II1 factors, the so-called diagonal subfactors (with cocycle). In the case when the cocycle is trivial these subfactors are well studied and their standard invariant (or planar algebra) is known. We give a description of the planar algebra of these subfactors when a cocycle is present. The action of Jones’ planar operad involves the 3-cocycle ω explicitly and some interesting identities for 3-cocycles appear when naturality of the action is verified.
منابع مشابه
Intermediate Subfactors with No Extra Structure
Let N ⊆ M be II1 factors with [M : N ] < ∞. There is a “standard invariant” for N ⊆ M , which we shall describe using the planar algebra formalism of [19]. The vector spaces Pk of N −N invariant vectors in the N −N bimodule ⊗M admit an action of the operad of planar tangles as in [19] and [21]. In more usual notation the vector space Pk is the relative commutant N ′ ∩Mk−1 in the tower Mk of [16...
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