\(E_6\) Turaev-Viro-Ocneanu invariant of lens space \(L(p,1)\) (Q2725568)

The Turaev-Viro-Ocneanu invariant of three-manifolds is a generalization of the Turaev-Viro invariant of three-manifolds, and it is derived from the paragroup of the subfactor. The author investigates the \(E_6\) Turaev-Viro-Ocneanu invariant derived from the \(E_6\) subfactor. He gives a formula for the invariant of the lens space \(L(p,1)\). The value of the \(E_6\) Turaev-Viro-Ocneanu invariant can be a complex number, in contrast to the fact that the value of the Turaev-Viro invariant must be a real number because of the relation ``Turaev-Viro invariant'' \(= |\)``Reshetikhin-Turaev invariant''\(|^2\). Thus the \(E_6\) Turaev-Viro-Ocneanu invariant can distinguish the lens space \(L(p,1)\) from the same one with reversed orientation \(L(p,p-1)\) for \(p=12k+3, 12k+4, 12k+8, 12k+9\) while the Turaev-Viro invariant can not.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00034].