Moduli space of filtered lambda-ring structures over a filtered ring

Details Moduli space of filtered lambda-ring structures over a filtered ring Moduli space of filtered lambda-ring structures over a filtered ring

2002-09-04

arxiv.org/abs/math/0209031v1

Int. J. Math. Math. Sci. (2004), no. 39, 2065-2084.

Mathematics

Algebraic Topology

23 pages

Scientific paper

Motivated by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered $\lambda$-ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first show that this set has a canonical topology compatible with the filtration on the given filtered ring. For power series rings $R \llbrack x \rrbrack$, where $R$ is between $\bZ$ and $\bQ$, with the $x$-adic filtration, we mimic the construction of the Lazard ring in formal group theory and show that the set of filtered $\lambda$-ring structures over $R \llbrack x \rrbrack$ is canonically isomorphic to the set of ring maps from some ``universal'' ring $U$ to $R$. From a local perspective, we demonstrate the existence of uncountably many mutually non-isomorphic filtered $\lambda$-ring structures over some filtered rings, including rings of dual numbers over binomial domains, (truncated) polynomial and powers series rings over torsionfree $\bQ$-algebras.

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