Automorphisms of subfactors from commuting squares

Svendsen, Anne

doi:10.1090/S0002-9947-04-03447-6

Automorphisms of subfactors from commuting squares
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by Anne Louise Svendsen PDF

Trans. Amer. Math. Soc. 356 (2004), 2515-2543 Request permission

Abstract:

We study an infinite series of irreducible, hyperfinite subfactors, which are obtained from an initial commuting square by iterating Jones’ basic construction. They were constructed by Haagerup and Schou and have $A_{\infty }$ as principal graphs, which means that their standard invariant is “trivial”. We use certain symmetries of the initial commuting squares to construct explicitly non-trivial outer automorphisms of these subfactors. These automorphisms capture information about the subfactors which is not contained in the standard invariant.

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