Free Incomplete Tambara Functors are Almost Never Flat-Reference-Cited by-同舟云学术

Free Incomplete Tambara Functors are Almost Never Flat

Published:2022-01-17 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Hill Michael A¹,Mehrle David²,Quigley James D²

Affiliation:

1. Department of Mathematics, University of California, Los Angeles, CA 90095, USA

2. Department of Mathematics, Cornell University, Ithaca, NY 14953, USA

Abstract

Abstract Free algebras are always free as modules over the base ring in classical algebra. In equivariant algebra, free incomplete Tambara functors play the role of free algebras and Mackey functors play the role of modules. Surprisingly, free incomplete Tambara functors often fail to be free as Mackey functors. In this paper, we determine for all finite groups conditions under which a free incomplete Tambara functor is free as a Mackey functor. For solvable groups, we show that a free incomplete Tambara functor is flat as a Mackey functor precisely when these conditions hold. Our results imply that free incomplete Tambara functors are almost never flat as Mackey functors. However, we show that after suitable localizations, free incomplete Tambara functors are always free as Mackey functors.

Funder

National Science Foundation

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnab361/42226417/rnab361.pdf

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