Necklace rings and logarithmic functions

Abstract: In this paper, we develop the theory of the necklace ring and the logarithmic function. Regarding the necklace ring, we introduce the necklace ring functor Nr from the category of special -rings into the category of special -rings and then study the associated Adams operators. As far as the logarithmic function is concerned, we generalize the results in Bryant''s paper [Free Lie algebras and formal power series, J. Algebra 253(1) (2002) 167–188] to the case of graded Lie (super)algebras with a group action by applying the Euler–Poincaré principle. [Copyright &y& Elsevier]