A Comparison of Takai and Treumann Dualities
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908579395534848 |
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| author | Nadig, Vikram |
| author_facet | Nadig, Vikram |
| contents | We prove a comparison result between two duality statements - Takai duality, which is implemented by the crossed product functor $- \rtimes G: KK^{G} \to KK^{\hat G}$ on equivariant Kasparov categories; and Treumann duality, which asserts the existence of an exotic equivalence of stable $\infty$-categories $\text{Mod}(KU_p[G])^{ft} \simeq \text{Mod}(KU_p[\hat G])^{ft}$ given by tensoring with a particular $(G,\hat G)$-bimodule $\textbf{M}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Comparison of Takai and Treumann Dualities Nadig, Vikram K-Theory and Homology Algebraic Topology Operator Algebras We prove a comparison result between two duality statements - Takai duality, which is implemented by the crossed product functor $- \rtimes G: KK^{G} \to KK^{\hat G}$ on equivariant Kasparov categories; and Treumann duality, which asserts the existence of an exotic equivalence of stable $\infty$-categories $\text{Mod}(KU_p[G])^{ft} \simeq \text{Mod}(KU_p[\hat G])^{ft}$ given by tensoring with a particular $(G,\hat G)$-bimodule $\textbf{M}$. |
| title | A Comparison of Takai and Treumann Dualities |
| topic | K-Theory and Homology Algebraic Topology Operator Algebras |
| url | https://arxiv.org/abs/2406.13212 |