Real and complex K-theory for higher rank graph algebras arising from cube complexes
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912244946698240 |
|---|---|
| author | Boersema, Jeffrey L Vdovina, Alina |
| author_facet | Boersema, Jeffrey L Vdovina, Alina |
| contents | Using the Evans spectral sequence and its counter-part for real $K$-theory, we compute both the real and complex $K$-theory of several infinite families of $C^*$-algebras based on higher-rank graphs of rank $3$ and $4$. The higher-rank graphs we consider arise from double-covers of cube complexes. By considering the real and complex $K$-theory together, we are able to carry these computations much further than might be possible considering complex $K$-theory alone. As these algebras are classified by $K$-theory, we are able to characterize the isomorphism classes of the graph algebras in terms of the combinatorial and number-theoretic properties of the construction ingredients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00298 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real and complex K-theory for higher rank graph algebras arising from cube complexes Boersema, Jeffrey L Vdovina, Alina Operator Algebras 46L80 (Primary), 19K99, 20E08 (Secondary) Using the Evans spectral sequence and its counter-part for real $K$-theory, we compute both the real and complex $K$-theory of several infinite families of $C^*$-algebras based on higher-rank graphs of rank $3$ and $4$. The higher-rank graphs we consider arise from double-covers of cube complexes. By considering the real and complex $K$-theory together, we are able to carry these computations much further than might be possible considering complex $K$-theory alone. As these algebras are classified by $K$-theory, we are able to characterize the isomorphism classes of the graph algebras in terms of the combinatorial and number-theoretic properties of the construction ingredients. |
| title | Real and complex K-theory for higher rank graph algebras arising from cube complexes |
| topic | Operator Algebras 46L80 (Primary), 19K99, 20E08 (Secondary) |
| url | https://arxiv.org/abs/2407.00298 |