Unshaded planar algebras and their associated II _1 factors

摘要

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 MP. We prove that MP is a II _1 factor that contains a generic maximal abelian subalgebra called the cup subalgebra.