A note on Green functors with inflation

Bartel, A. and Spencer, M. (2017) A note on Green functors with inflation. Journal of Algebra, 483, pp. 230-244. (doi: 10.1016/j.jalgebra.2017.03.031)

149643.pdf - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.



This note is motivated by the problem to understand, given a commutative ring F, which G-sets X, Y give rise to isomorphic F[G]-representations F[X]≅F[Y]. A typical step in such investigations is an argument that uses induction theorems to give very general sufficient conditions for all such relations to come from proper subquotients of G. In the present paper we axiomatise the situation, and prove such a result in the generality of Mackey functors and Green functors with inflation. Our result includes, as special cases, a result of Deligne on monomial relations, a result of the first author and Tim Dokchitser on Brauer relations in characteristic 0, and a new result on Brauer relations in characteristic p > 0. We will need the new result in a forthcoming paper on Brauer relations in positive characteristic.

Item Type:Articles
Additional Information:During parts of this project, the first author was partially supported by a Research Fellowship from the Royal Commission for the Exhibition of 1851, and by EPSRC Grant EP/N006542/1, and the second author is supported by an EPSRC Doctoral Grant.
Glasgow Author(s) Enlighten ID:Bartel, Professor Alex
Authors: Bartel, A., and Spencer, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Algebra
ISSN (Online):1090-266X
Published Online:11 April 2017
Copyright Holders:Copyright © 2017 Elsevier Inc.
First Published:First published in Journal of Algebra 483: 230-244
Publisher Policy:Reproduced in accordance with the publisher copyright policy
Related URLs:

University Staff: Request a correction | Enlighten Editors: Update this record