E₆ TURAEV-VIRO-OCNEANU INVARIANT OF LENS SPACE L(p, 1)

The Turaev-Viro-Ocneanu invariant of three manifolds is a generalization of the Turaev-Viro invariant of three manifolds, and is derived from the paragroup of the subfactor. We investigate the E₆ Turaev-Viro-Ocneanu invariant derived from the E₆ subfactor. We give a formula for the invariant of the lens space L(p, 1). The value of the E₆ Turaev-Viro-Ocneanu invariant can be a complex number, in contrast with 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 E₆ 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.