Rosenberg's conjecture for the first negative $K$-group
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866910604183207936 |
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| author | Aoki, Ko |
| author_facet | Aoki, Ko |
| contents | Based on his claims in 1990, Rosenberg conjectured in 1997 that the negative algebraic $K$-groups of C*-algebras are invariant under continuous homotopy. Contrary to his expectation, we prove that such invariance holds for $K_{-1}$ of arbitrary Banach rings by establishing a certain continuity result. We also construct examples demonstrating that similar continuity results do not hold for lower $K$-groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09651 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rosenberg's conjecture for the first negative $K$-group Aoki, Ko Operator Algebras Complex Variables K-Theory and Homology Based on his claims in 1990, Rosenberg conjectured in 1997 that the negative algebraic $K$-groups of C*-algebras are invariant under continuous homotopy. Contrary to his expectation, we prove that such invariance holds for $K_{-1}$ of arbitrary Banach rings by establishing a certain continuity result. We also construct examples demonstrating that similar continuity results do not hold for lower $K$-groups. |
| title | Rosenberg's conjecture for the first negative $K$-group |
| topic | Operator Algebras Complex Variables K-Theory and Homology |
| url | https://arxiv.org/abs/2409.09651 |