We consider compact group actions on C*- and W*-algebras. We prove results that relate the duality property of the action (as defined in the Introduction) with other relevant properties of the system such as the relative commutant of the fixed point algebras being trivial (called the irreducibility of the inclusion) and also to the Galois correspondence between invariant C*-subalgebras containing the fixed point algebra and the class of closed normal subgroups of the compact group.

中文翻译：

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算子代数和应用上紧群作用的对偶性：不可约包含和伽罗瓦对应

我们考虑 C*- 和 W*- 代数上的紧群动作。我们证明了将动作的对偶属性（如引言中定义）与系统的其他相关属性相关的结果，例如不动点代数的相对交换是微不足道的（称为包含的不可约性）以及伽罗瓦包含不动点代数的不变 C*-子代数与紧群的闭正规子群类之间的对应关系。