On Distributive Subfactor Planar Algebras

<strong>Mathematics Seminar of the School of Physical Sciences ---------------------------------------------------------</strong> Title:&nbsp;<strong>On Distributive Subfactor Planar Algebras</strong> Speaker:&nbsp;<strong>Sebastien Palcoux&nbsp;</strong> (Institute of Mathematical Sciences, Chennai) Date:&nbsp;<strong>September 22, 2016</strong> <strong>Abstract:&nbsp;</strong>A theorem of Oystein Ore states that a finite group is cyclic iff its subgroups lattice is distributive. A subfactor planar algebra is called distributive if its biprojections lattice is distributive. We define an Euler totient for such planar algebras, which exactly extends Euler's totient of natural numbers. We then extend one side of Ore's theorem to distributive subfactor planar algebras with a nonzero Euler totient, i.e. we prove the existence of a (2-box) minimal projection generating the identity biprojection. We plan to prove that the Euler totient of any distributive subfactor planar algebra is nonzero.