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arXiv · 1202.1298

Unshaded planar algebras and their associated II_1 factors

Arnaud Brothier
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Abstract

Guionnet et al. gave a construction of a II_1 factor associated to a subfactor planar algebra. In this paper we define an unshaded planar algebra. To any unshaded planar algebra P we associate a finite von Neumann algebra M_P. We prove that M_P is a II_1 factor that contains a generic maximal abelian subalgebra called the cup subalgebra.

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Arnaud Brothier. 2012-02-06. Unshaded planar algebras and their associated II_1 factors. https://arxiv.org/abs/1202.1298

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