## More Homological Approach to Composition of Subfactors

J. Math. Sci. Univ. Tokyo
Vol. 10 (2003), No. 4, Page 599--630.

Masuoka, Akira
More Homological Approach to Composition of Subfactors
By using homological tools in \cite{M4}, we refine in a slightly generalized form the result by Izumi and Kosaki \cite{IK} which classifies outer actions of a matched pair of finite groups on the hyperfinite $II_{1}$ factor. An analogous result on outer weak actions is proved. We naturally connect outer (weak) actions with Galois extensions for Hopf (or Kac) algebras or coquasi-Hopf algebras.