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A note on twisted group rings and semilinearization

2021/02/12 by Brazelton, Thomas
#Algebraic Topology (math.AT) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2102.06723

Abstract

In this short note, we construct a right adjoint to the functor which associates to a ring R equipped with a group action its twisted group ring. This right adjoint admits an interpretation as semilinearization, in that it sends an R-module to the group of semilinear R-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.

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