In this paper, we investigate if the presence of symmetries in the evolution of an open quantum system gives information about the invariant subspaces. Unfortunately, the answer is, in general, negative, but under suitable conditions we can observe that the representation through which we describe the symmetry determines a privileged family of orthogonal projections strongly correlated with the structure of the decoherence-free sub-algebra and, as a consequence, with harmonic projections.

中文翻译：

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关于协方差与量子马尔可夫半群的无退相干子代数的关系

在本文中，我们研究了开放量子系统演化中对称性的存在是否提供了有关不变子空间的信息。不幸的是，答案通常是否定的，但在适当的条件下，我们可以观察到我们用来描述对称性的表示确定了一个特权族的正交投影，它与无退相干子代数的结构密切相关，并且，作为结果，带有谐波预测。