A simple sufficient condition for triviality of obstruction in the orbifold construction for subfactors

TL;DR

This paper introduces a straightforward criterion to determine when obstructions are trivial in the orbifold construction for subfactors, enabling the construction of specific subfactors with certain principal graphs.

Contribution

It provides a new simple sufficient condition for triviality of obstruction in orbifold construction, simplifying the process of constructing subfactors with particular principal graphs.

Findings

Established a simple sufficient condition for trivial obstruction

Demonstrated existence of subfactors with principal graph D_{2n}

Reduced reliance on complex paragroup theory

Abstract

We present a simple sufficient condition for triviality of obstruction in the orbifold construction. As an application, we can show the existence of subfactors with principal graph $D_{2n}$ without full use of Ocneanu's paragroup theory.