Abstract
A combination of the geometric spectral theory (based on a pair of an order-unit space and a base-norm space) with the theory of invariant cones in Lie algebras can replace the associative *-algebras as a complete description of dynamical systems. This geometric language is equally applicable to the classical and quantum cases. Reversing the relation between the automorphism groups of the two relevant structures-(lattice) order and Lie product-one may obtain a large class of new (quantum) dynamical systems.
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