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Quantum spectral symmetries. (English) Zbl 1387.81232
Summary: Quantum symmetries of spectral lattices are studied. Basic properties of spectral order on $$AW^\ast$$-algebras are summarized. Connection between projection and spectral automorphisms is clarified by showing that, under mild conditions, any spectral automorphism is a composition of function calculus and Jordan $$\ast$$-automorphism. Complete description of quantum spectral symmetries on Type I and Type II $$AW^\ast$$-factors are completely described.

##### MSC:
 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 46L05 General theory of $$C^*$$-algebras 46L40 Automorphisms of selfadjoint operator algebras
##### Keywords:
spectral order; $$AW^\ast$$-algebras; preserves
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##### References:
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