A note on the crossed product R（A, α） associated with PSL2（R）

作     者：WU WenMing 1 School of Mathematical and Computer Science, Chongqing Normal University, Chongqing 400047, China 2 Department of Mathematical Science, Tsinghua University, Beijing 100084, China 

出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))

年 卷 期：2008年第11期

页      面：2081-2088页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：the Youth Foundation of Sichuan Education Department of China (Grant No.2003B017) 

主　　题：crossed product rational actions PSL2(R) von Neumann algebras 

摘      要：Given the hyperbolic measure dxdy/y2 on the upper half plane H, the rational actions of PSL2(R) on H induces a continuous unitary representation α of this group on the Hilbert space L2(H, dxdy/y2). Supposing that A = {Mf : f ∈ L∞(H, dxdy/y2)}, we show that the crossed product R(A,α) is of type I. In fact, the crossed product R(A,α) is *-isomorphic to the von Neumann algebra B(L2(P,ν))■LK, where LK is the abelian group von Neumann algebra generated by the left regular representation of K.