- December 2021
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- 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.
- positive maps; groupoid-algebras; 2-groupoids; functions of positive-type