关于离散群的半直积与von Neumann代数的交叉积

On Semidirect Product of Discrete Groups and Crossed Product of von Neumann Algebras

本文证明了离散群G与H的半直积G×_σH的群von Neumann代数有L_G×_σH≌L_G×_σH．并且当α是酉实现时,证明了交叉积M×_α(G×_σH)与交叉积(M×_αG)×_αH同构．

In this article, we show that the group von Neumann algebra LG×σH is isomorphic to the crossed product LG×σH , where G and H are discrete groups. Furthermore, when a is unitary implemented, then M×α（G×αH）is isomorphic to （M×αG）×αH for any yon Neumann algebra