An example of Kac algebra actions on von Neumann algebras

Yamanouchi, Takehiko

doi:10.1090/S0002-9939-1993-1150659-5

An example of Kac algebra actions on von Neumann algebras
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Proc. Amer. Math. Soc. 119 (1993), 503-511 Request permission

Abstract:

By using Majid’s bicrossproduct Kac algebra, a nontrivial example of an action of a Kac algebra on a von Neumann algebra is given. It is shown that the actions constructed are ergodic. The crossed products by the actions are examined.

References

Michel Enock, Produit croisé d’une algèbre de von Neumann par une algèbre de Kac, J. Functional Analysis 26 (1977), no. 1, 16–47 (French, with English summary). MR 0473854, DOI 10.1016/0022-1236(77)90014-3
Michel Enock and Jean-Marie Schwartz, Une dualité dans les algèbres de von Neumann, Supplément au Bull. Soc. Math. France, Tome 103, no. 4, Société Mathématique de France, Paris, 1975 (French). Bull. Soc. Math. France Mém., No. 44. MR 0442710
Shahn Majid, Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts, and the classical Yang-Baxter equations, J. Funct. Anal. 95 (1991), no. 2, 291–319. MR 1092128, DOI 10.1016/0022-1236(91)90031-Y
Yoshiomi Nakagami and Masamichi Takesaki, Duality for crossed products of von Neumann algebras, Lecture Notes in Mathematics, vol. 731, Springer, Berlin, 1979. MR 546058, DOI 10.1007/BFb0069742
Jean-Marie Schwartz, Sur la structure des algèbres de Kac. I, J. Functional Analysis 34 (1979), no. 3, 370–406 (French, with English summary). MR 556262, DOI 10.1016/0022-1236(79)90083-1
Jean-Marie Schwartz, Sur la structure des algèbres de Kac. I, J. Functional Analysis 34 (1979), no. 3, 370–406 (French, with English summary). MR 556262, DOI 10.1016/0022-1236(79)90083-1
Masamichi Takesaki, Duality for crossed products and the structure of von Neumann algebras of type III, Acta Math. 131 (1973), 249–310. MR 438149, DOI 10.1007/BF02392041
Takehiko Yamanouchi, The intrinsic group of Majid’s bicrossproduct Kac algebra, Pacific J. Math. 159 (1993), no. 1, 185–199. MR 1211392, DOI 10.2140/pjm.1993.159.185