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Articles

Gluing of endopermutation modules

Pages 4904-4921 | Received 13 Feb 2020, Accepted 20 May 2020, Published online: 26 Jun 2020
 

Abstract

We introduce the notion of Frobenius-friendly categories and obtain the slash functors on these categories. Let G be a finite p-group. We give a local construction of the O-stable category of a big enough Frobenius-friendly category C of OG-modules: an endopermutation OG-module in C gives rise, via slash functors, to a family of endopermutation kNG(Q)/Q-modules, where Q runs over non-trivial subgroups of G, together with certain isomorphisms. Conversely, the data of a suitable compatible family of endopermutation kNG(Q)/Q-modules {VQ}Q comes from an endopermutation OG-module in C, unique up to isomorphism in the O-stable category.

2010 Mathematics Subject Classification:

Acknowledgments

The author thanks the referee for helpful comments and suggestions which contributed to a significant improvement in the presentation of the paper.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The author is supported by the Program of Cultivation of Excellent Doctoral dissertation of CCNU (2019YBZZ063).

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