A Comparison of Takai and Treumann Dualities

Fuente: arXiv
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1. Verfasser: Nadig, Vikram
Format: Preprint
Veröffentlicht: 2024
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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