A general Greenlees-May splitting principle
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911892173225984 |
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| author | Bouc, Serge Dell'Ambrogio, Ivo Martos, Rubén |
| author_facet | Bouc, Serge Dell'Ambrogio, Ivo Martos, Rubén |
| contents | In equivariant topology, Greenlees and May used Mackey functors to show that, rationally, the stable homotopy category of $G$-spectra over a finite group $G$ splits as a product of simpler module categories. We extend the algebraic part (also independently proved by Thévenaz and Webb) of this classical result to Mackey modules over an arbitrary Green functor, and use the case of the complex representation ring Green functor to obtain an algebraic model of the rational equivariant Kasparov category of $G$-cell algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18885 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A general Greenlees-May splitting principle Bouc, Serge Dell'Ambrogio, Ivo Martos, Rubén K-Theory and Homology Algebraic Topology Operator Algebras 20C99, 19K35, 19L47, 55Q91 In equivariant topology, Greenlees and May used Mackey functors to show that, rationally, the stable homotopy category of $G$-spectra over a finite group $G$ splits as a product of simpler module categories. We extend the algebraic part (also independently proved by Thévenaz and Webb) of this classical result to Mackey modules over an arbitrary Green functor, and use the case of the complex representation ring Green functor to obtain an algebraic model of the rational equivariant Kasparov category of $G$-cell algebras. |
| title | A general Greenlees-May splitting principle |
| topic | K-Theory and Homology Algebraic Topology Operator Algebras 20C99, 19K35, 19L47, 55Q91 |
| url | https://arxiv.org/abs/2405.18885 |