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Examples of one-parameter automorphism groups of UHF algebras

Akitaka Kishimoto
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Abstract

Examples of (strongly continuous) one-parameter groups of automorphisms of UHF C*-algebras are given. One example has the property that the infinitesimal generator does not have a union of finite-dimensional subalgebras as a core. (This solves the so-called core problem, raised by S. Sakai, in the negative.) The other has the property of not being classical or commutative, i.e., the one-parameter group is not just an inner perturbation of a one-parameter group which has an increasing sequence of invariant finite-dimensional subalgebras with dense union. (This was certainly expected but has not been proven explicitly.)

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Akitaka Kishimoto. 2000-08-01. Examples of one-parameter automorphism groups of UHF algebras. https://doi.org/10.1007/s002200000335

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