# Journal of Operator Theory

Volume 37, Issue 2, Spring 1997 pp. 281-302.

Composition of subfactors and twisted bicrossed products**Authors**: Jeong Hee Hong (1) and Wojciech SzymaĆski (2)

**Author institution:**(1) Department of Applied Mathematics, Korea Maritime University, Pusan, 606-791, KOREA. E-mail: hongjh@hanara.kmaritime.ac.kr

(2) Department of Mathematics, The University of Newcastle, Newcastle, NSW 2308, AUSTRALIA. E-mail: wojciech@frey.newcastle.edu.au

**Summary:**Subfactors of the form $\mathbb P^H \subset \mathbb P \rtimes K$, where H, K are finite groups of outer automorphisms of a finite factor $\mathbb P$, are studied. The corresponding Jones tower and some relative commutants are explicitly described. Hopf *-algebras related to the depth 2 case are calculated. These turn out to have the structure of cocycle twisted bicrossed products. Definitions, properties, and several examples of such twisted bicrossed products are given.

**Keywords:**Subfactor, Hopf algebra, twisted bicrossed product.

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