Groupoid Dynamical Systems and Crossed Product, II — The Case of -Systems

  • Tetsuya Masuda

    Kyoto University, Japan

Abstract

By analogy with -dynamical system, we define a -groupoid dynamical system where is a -algebra, is a locally compact groupoid, and is a continuous groupoid homomorphism. The groupoid crossed product is defined and is shown to have similar properties as the case of a group action. As a special case of this situation, if is a continuous homomorphism from to a locally compact group , we obtain groupoid dynamical system . In this case, there exists a co-action of on and the groupoid crossed product is isomorphic to the co-crossed product of by . The results in this paper is obtained by the analogy with our previous results for the case of -systems.

Cite this article

Tetsuya Masuda, Groupoid Dynamical Systems and Crossed Product, II — The Case of -Systems. Publ. Res. Inst. Math. Sci. 20 (1984), no. 5, pp. 959–970

DOI 10.2977/PRIMS/1195180874