R-analogue of the Burnside ring of profinite groups and free Lie algebras

초록

Let R be a finite-dimensional torsion-free special lambda-ring. In this paper we generalize the results in Dress and Siebeneicher (Adv. in Math. 70 (1988) 89; 78 (1989) 1) by constructing R-analogue Omega(R)(G) of the Burnside ring of profinite groups Omega(G). In particular, we remark that the (Grothendieck) Lie-module denominator identity of free Lie algebras in Oh (Necklace rings and logarithmic functions, preprint, KIAS, 2003) is closely related to the canonical isomorphism between Omega(R)(G) and Grothendieck's ring of formal power series with coefficients in R and constant term 1. (C) 2003 Elsevier Inc. All rights reserved.

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