Starting from the canonical symmetroid 𝒮(G) associated with a groupoid G, the issue of describing dynamical maps in the groupoidal approach to quantum mechanics is addressed. After inducing a Haar measure on the canonical symmetroid 𝒮(G), the associated von Neumann groupoid algebra is constructed. It is shown that the left-regular representation allows to define linear maps on the groupoid-algebra of the groupoid G and given subsets of functions are associated with completely positive maps. Some simple examples are also presented.

中文翻译：

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动态映射和对称

从规范对称开始𝒮(G)与 groupoid 相关联G，解决了在量子力学的群面方法中描述动力学映射的问题。在规范对称性上诱导 Haar 测度后𝒮(G)，构造了相关的冯诺依曼群代数。结果表明，左正则表示允许在 groupoid 的 groupoid-algebra 上定义线性映射G并且给定的函数子集与完全正映射相关联。还介绍了一些简单的例子。