Automorphisms and Derivations
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With this chapter, we start the application of local multipliers to the study of operators on C*-algebras. Among the most important classes of linear mappings on C*-algebras are automorphisms and derivations. In physical terms, that is, if the self-adjoint part of a C*-algebra serves as the set of observables of a quantum system, automorphisms correspond to the symmetries, while one-parameter automorphism groups describe the reversible time evolution of the system (in the Heisenberg picture). Their infinitesimal generators are the derivations, which also play an important role in the structure theory of C*-algebras, notably in cohomology theory.
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