Publications of the Research Institute for Mathematical Sciences


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Volume 31, Issue 3, 1995, pp. 481–517
DOI: 10.2977/prims/1195164051

Classification of Paragroup Actions on Subfactors

Yasuyuki Kawahigashi[1]

(1) Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, 153-8914, TOKYO, JAPAN

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 MM1 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.

Keywords:

Kawahigashi Y. Classification of Paragroup Actions on Subfactors. Publ. Res. Inst. Math. Sci. 31 (1995), 481-517. doi: 10.2977/prims/1195164051