Mackey structures on equivariant algebraic K-theory

Kazuhisa Shimakawa

doi:10.1007/BF00535646

Mackey structures on equivariant algebraic K-theory

Kazuhisa Shimakawa

Graduate School of Natural Science and Technology

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We study the Mackey structure of the G-spectrum K_GC associated to a monoidal G-category C. It is proved that the coefficient system of K_GC coincides, as a (graded) Mackey functor, with the system of equivariant K-groups in the sense of Fröhlich and Wall. It is also shown that for any exact category U, there exists a G-spectrum Q_GU representing the equivariant K-theory of U in the sense of Dress and Kuku, and that Q_GU is naturally G-homotopy equivalent to K_GIso U if every short exact sequence in U splits.

Original language	English
Pages (from-to)	355-371
Number of pages	17
Journal	K-Theory
Volume	5
Issue number	4
DOIs	https://doi.org/10.1007/BF00535646
Publication status	Published - Jul 1 1991

Keywords

G-spectrum
Special Γ-space
equivariant algebraic K-theory

ASJC Scopus subject areas

Mathematics(all)

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10.1007/BF00535646

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AB - We study the Mackey structure of the G-spectrum KGC associated to a monoidal G-category C. It is proved that the coefficient system of KGC coincides, as a (graded) Mackey functor, with the system of equivariant K-groups in the sense of Fröhlich and Wall. It is also shown that for any exact category U, there exists a G-spectrum QGU representing the equivariant K-theory of U in the sense of Dress and Kuku, and that QGU is naturally G-homotopy equivalent to KGIso U if every short exact sequence in U splits.

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Mackey structures on equivariant algebraic K-theory

Abstract

Keywords

ASJC Scopus subject areas

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