Examples of one-parameter automorphism groups of UHF algebras
Operator Algebras
2009-10-31 v1
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.)
Keywords
Cite
@article{arxiv.math/0008003,
title = {Examples of one-parameter automorphism groups of UHF algebras},
author = {Akitaka Kishimoto},
journal= {arXiv preprint arXiv:math/0008003},
year = {2009}
}
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16 pages