JournalsprimsVol. 31 , No. 3DOI 10.2977/prims/1195164051

Classification of Paragroup Actions on Subfactors

  • Yasuyuki Kawahigashi

    University of Tokyo, Japan
Classification of Paragroup Actions on Subfactors cover

Abstract

We define "a crossed product by a paragroup action on a subfactor" as a certain commuting square of type II1 factors and give their complete classification in a strongly amenable case (in the sense of S. Popa) in terms of a new combinatorial object which generalizes Ocneanu's paragroup. As applications, we show that the subfactor NM of Goodman-de la Harpe-Jones with index 3 + √ 3 is not conjugate to its dual M ⊂ _M_1 by showing the fusion algebras of N-N bimodules and M-M bimodules are different, although the principal graph and the dual principal graph are the same. We also make an analogue of the coset construction in RCFT for subfactors in our settings.