Invariantly ordered spectral Lie algebras as abstract dynamical systems (Q584368)

Here the author explains his new definition of a dynamical system. Motivated by the mathematical formulation of quantum mechanics and classical mechanics in terms of \(C^*\)-algebras and Lie algebras he introduces ordered Lie algebras which admit a spectral theory in the sense of \textit{E. M. Alfsen} and \textit{F. W. Shultz} [Mem. Am. Math. Soc. 172 (1976; Zbl 0337.46013)] and for which the order structure is compatible with the Lie algebra structure.