Witt–Burnside ring and Burnside ring over a special λ-ring

Abstract

Given an arbitrary group G, we construct a covariant functor FˆG from the category of special λ-rings to that of commutative rings with unity. When G is a strongly complete profinite group, it will be used to reconstruct the functor NrG, which was first introduced in [Y.-T. Oh, R-analogue of the Burnside ring of profinite groups and free Lie algebras, Adv. Math. 190 (2005) 1–46] to investigate the structure of Witt–Burnside rings over special λ-rings. More precisely, given a special λ-ring R, we show that NrG(R) is functorially isomorphic to FˆG(R)/JG(R) for some ideal JG(R) of FˆG(R). The connection to the functor FG due to [J.J. Graham, Generalized Witt vectors, Adv. Math. 99 (1993) 248–263] will also be demonstrated.