We prove that the flatness condition in Ocneanu's paragroup theory for graphs with depth two is equivalent to existence of the multiplicative unitaries in the theory of Baaj-Skandalis by using "Fourier transform" introduced by A. Ocneanu. Moreover, from two Kac algebras dual to each other, we construct a subfactor as a crossed product by a Kac algebra action, with the string algebra construction.
Cite this article
Nobuya Sato, Fourier Transform for Paragroups and Its Application to the Depth Two Case. Publ. Res. Inst. Math. Sci. 33 (1997), no. 2, pp. 189–222DOI 10.2977/PRIMS/1195145447