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