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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Local subgroups and the stable category


Author: Wayne W. Wheeler
Journal: Trans. Amer. Math. Soc. 354 (2002), 2187-2205
MSC (2000): Primary 20C20
DOI: https://doi.org/10.1090/S0002-9947-02-02964-1
Published electronically: February 14, 2002
MathSciNet review: 1885649
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Abstract: If $G$ is a finite group and $k$ is an algebraically closed field of characteristic $p>0$, then this paper uses the local subgroup structure of $G$to define a category $\mathfrak{L}(G,k)$ that is equivalent to the stable category of all left $kG$-modules modulo projectives. A subcategory of $\mathfrak{L}(G,k)$ equivalent to the stable category of finitely generated $kG$-modules is also identified. The definition of $\mathfrak{L}(G,k)$ depends largely but not exclusively upon local data; one condition on the objects involves compatibility with respect to conjugations by arbitrary group elements rather than just elements of $p$-local subgroups.


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Additional Information

Wayne W. Wheeler
Affiliation: Center for Communications Research, 4320 Westerra Court, San Diego, California 92121
Email: wheeler@member.ams.org

DOI: https://doi.org/10.1090/S0002-9947-02-02964-1
Received by editor(s): January 2, 2001
Received by editor(s) in revised form: September 24, 2001
Published electronically: February 14, 2002
Article copyright: © Copyright 2002 American Mathematical Society