Paper-folding models for the CAR algebra
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908480797933568 |
|---|---|
| author | Kopsacheilis, Grigoris Winter, Wilhelm |
| author_facet | Kopsacheilis, Grigoris Winter, Wilhelm |
| contents | We show that the CAR algebra admits a Cantor spectrum C*-diagonal that is not conjugate to the standard AF diagonal. We obtain this by classification theory of C*-algebras, and the diagonal arises by realising the CAR algebra as the crossed product of a free minimal action on the Cantor space, where the acting group is the product of a locally finite group with the infinite dihedral group. The main ingredient in the construction is a binary subshift associated to the well-known regular paper-folding sequence.
Moreover, we show that the CAR algebra in fact admits countably many, pairwise non-conjugate, Cantor spectrum diagonals which are distinguished by the different values of their diagonal dimension, as defined by Li, Liao and the second named author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Paper-folding models for the CAR algebra Kopsacheilis, Grigoris Winter, Wilhelm Operator Algebras Dynamical Systems Functional Analysis We show that the CAR algebra admits a Cantor spectrum C*-diagonal that is not conjugate to the standard AF diagonal. We obtain this by classification theory of C*-algebras, and the diagonal arises by realising the CAR algebra as the crossed product of a free minimal action on the Cantor space, where the acting group is the product of a locally finite group with the infinite dihedral group. The main ingredient in the construction is a binary subshift associated to the well-known regular paper-folding sequence. Moreover, we show that the CAR algebra in fact admits countably many, pairwise non-conjugate, Cantor spectrum diagonals which are distinguished by the different values of their diagonal dimension, as defined by Li, Liao and the second named author. |
| title | Paper-folding models for the CAR algebra |
| topic | Operator Algebras Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2508.04837 |