Jump transformations and an embedding of ${\cal O}_{\infty}$ into ${\cal O}_{2}$

Details Jump transformations and an embedding of ${\cal O}_{\infty}$ into ${\cal O}_{2}$ Jump transformations and an embedding of ${\cal O}_{\infty}$ into ${\cal O}_{2}$

2008-09-27

arxiv.org/abs/0809.4800v1

Mathematics

Operator Algebras

15 pages 6 figures

Scientific paper

10.1063/1.3081386

A measurable map $T$ on a measure space induces a representation $\Pi_{T}$ of a Cuntz algebra ${\cal O}_{N}$ when $T$ satisfies a certain condition. For such two maps $\tau$ and $\sigma$ and representations $\Pi_{\tau}$ and $\Pi_{\sigma}$ associated with them, we show that $\Pi_{\tau}$ is the restriction of $\Pi_{\sigma}$ when $\tau$ is a jump transformation of $\sigma$. Especially, the Gauss map $\tau_1$ and the Farey map $\sigma_1$ induce representations $\Pi_{\tau_1}$ of ${\cal O}_{\infty}$ and that $\Pi_{\sigma_1}$ of ${\cal O}_{2}$, respectively, and $\Pi_{\tau_1}=\Pi_{\sigma_1}|_{{\cal O}_{\infty}}$ with respect to a certain embedding of ${\cal O}_{\infty}$ into ${\cal O}_{2}$.

Affiliated with

Also associated with

No associations

Rating

Jump transformations and an embedding of ${\cal O}_{\infty}$ into ${\cal O}_{2}$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Jump transformations and an embedding of ${\cal O}_{\infty}$ into ${\cal O}_{2}$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Jump transformations and an embedding of ${\cal O}_{\infty}$ into ${\cal O}_{2}$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-353406