English

UHF flows and the flip automorphism

Operator Algebras 2009-10-31 v1 Mathematical Physics math.MP

Abstract

A UHF flow is an infinite tensor product type action of the reals on a UHF algebra AA and the flip automorphism is an automorphism of AAA\otimes A sending xyx\otimes y into yxy\otimes x. If α\alpha is an inner perturbation of a UHF flow on AA, there is a sequence (un)(u_n) of unitaries in AAA\otimes A such that αtαt(un)un\alpha_t\otimes \alpha_t(u_n)-u_n converges to zero and the flip is the limit of \Adun\Ad u_n. We consider here whether the converse holds or not and solve it with an additional assumption: If AAAA\otimes A\cong A and α\alpha absorbs any UHF flow β\beta (i.e., αβ\alpha\otimes\beta is cocycle conjugate to α\alpha), then the converse holds; in this case α\alpha is what we call a universal UHF flow.

Keywords

Cite

@article{arxiv.math/0011140,
  title  = {UHF flows and the flip automorphism},
  author = {A. Kishimoto},
  journal= {arXiv preprint arXiv:math/0011140},
  year   = {2009}
}

Comments

18 pages