#### Alladi Ramakrishnan Hall

#### Generalization of a theorem of Oystein Ore from groups to subfactor planar algebras: an easy route to the wonderland of "quantum arithmetic"

#### Sebastien Palcoux

##### IMSc

*Oystein Ore proved in 1938 that a finite group is cyclic iff its subgroups lattice is distributive. A (subfactor) planar algebra is an extension of the notion of group (much beyond the notion of quantum group). We will present our result generalizing Ore's theorem to the subfactor planar algebras. Then we will give an overview of the nascent "cyclic subfactor theory" (from which our result emerged) which is a kind of quantum extension of the arithmetic of natural numbers.*

Content:

1. Ore's theorem for groups and inclusions

2. Subfactors and planar algebras

3. Ore's theorem for subfactor planar algebras

4. Cyclic subfactors : a "quantum arithmetic"

Done