Unshaded planar algebras and their associated II₁ factors

2012/02/06 by Brothier, Arnaud
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1202.1298

Abstract

Guionnet et al. gave a construction of a II₁ 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 II₁ factor that contains a generic maximal abelian subalgebra called the cup subalgebra.

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