A note on twisted group rings and semilinearization
Abstract
In this short note, we construct a right adjoint to the functor which associates to a ring equipped with a group action its twisted group ring. This right adjoint admits an interpretation as semilinearization, in that it sends an -module to the group of semilinear -module automorphisms of the module. As an immediate corollary, we provide a novel proof of the classical observation that modules over a twisted group ring are modules over the base ring together with a semilinear action.
Cite
@article{arxiv.2102.06723,
title = {A note on twisted group rings and semilinearization},
author = {Thomas Brazelton},
journal= {arXiv preprint arXiv:2102.06723},
year = {2021}
}
Comments
This note, to appear in Communications in Algebra, was initially was an appendix to "Homotopy Mackey functors of equivariant algebraic K-theory," but was more elaborate than what was strictly needed in that paper. Since this may be an observation of independent interest in algebra, it has been written up separately