\(R\)-analogue of the Burnside ring of profinite groups and free Lie algebras
Let \(G\) be a profinite group. The author generalizes results of \textit{A. W. M. Dress} and \textit{C. Siebeneicher} [Adv. Math. 70, 87--132 (1988; Zbl 0691.13026); ibid. 78, 1--41 (1989; Zbl 0691.13020)]. If \(R\) is a finite-dimensional torsionfree special \(\lambda\)-ring, he constructs an \(R\)-analogue of the completeted Burnside ring of profinite groups, say \(\Omega_R(G)\). [In the corrigendum a new definition of \(\Omega_R(G)\) is given.] He remarks that the Lie-module denominator identity for free Lie algebras [\textit{Y.-T. Oh}, Adv. Math. 205, 434--486 (2006; Zbl 1105.19002)] is closely related to the canonical isomorphism between \(\Omega_R(G)\) and the Grothendieck ring of formal power series with coefficients in \(R\) and constant term 1. Some identities in this paper can be interpreted in combinatorial form by the \(R\)-necklace ring of \(G\) [loc. cit. (2006)].
scientific article; zbMATH DE number 2126443
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