Year: 2026
Type: preprint
Abstract: We define an intrinsic unital completely positive (ucp) map from the Cuntz algebra to the Pythagorean with finitely many generators. This permits to lift states and cyclic representations. This process restricts to the Cuntz-Toeplitz algebras and the contraction algebras. Taking inductive limits we obtain an effective machinery for constructing states on the infinite Cuntz algebra $\mathcal O_\infty$. Combining this approach with previous techniques of the first author we obtain large families of pairwise inequivalent irreducible representations of $\mathcal O_\infty$: one family being in an obvious bijection with the unit sphere of Hilbert's space.
Source: arXiv (Cornell University)
Authors: Brothier, Arnaud, Evans, David. E.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220963385