科研之友
微信
新浪微博
Facebook
分享链接
摘要
Given the hyperbolic measure dxdy/y(2) on the upper half plane H, the rational actions of PSL(2)(R) on H induces a continuous unitary representation a of this group on the Hilbert space L(2)(H, dxdy/y(2)). Supposing that A = {Mf : f epsilon L(infinity)(H, dxdy/y(2))}, we show that the crossed product R(A, alpha) is of type I. In fact, the crossed product R(A, alpha) is *- isomorphic to the von Neumann algebra B(L(2)( P, nu)) (circle times) over bar L(K), where L(K) is the abelian group von Neumann algebra generated by the left regular representation of K.
