有限型共变系统的交叉积

Crossed Product for Covariant Systems of Finite Type

交叉积是通过共变系统生成von Neumann代数的有力工具.经典情形下,von Neumann代数交叉积的作用空间非常抽象.为使其作用空间更加简单,定义了有限型共变系统,通过这个系统构造的von Neumann代数与经典情形同构,从而给出有限型共变系统交叉积的简明刻画.

Crossed product is a powerful tool in generating von Neumann algebras from covariant systems. In classical cases, the action space of avon Neumann algebra from a crossed product is extremely abstract. In order to make the action space simple, a covariant system of finite type was defined. In the system a concise characterization of the crossed product was given by constructing a new von Neumann algebra, which is isomorphic to the algebra from the classical case.