Moduli space of filtered \(\lambda\)-ring structures over a filtered ring.
type: Item
instance of: scholarly article
title: Moduli space of filtered \(\lambda\)-ring structures over a filtered ring.
zbMATH Open document ID: 1108.16039
DOI: 10.1155/S0161171204304138
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0209031
full work available at URL: https://eudml.org/doc/53056
review text: Summary: Motivated in part 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 \(R[\![x]\!]\), where \(R\) is between \(\mathbb{Z}\) and \(\mathbb{Q}\), 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 \(R[\![x]\!]\) 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 nonisomorphic filtered \(\lambda\)-ring structures over some filtered rings, including rings of dual numbers over binomial domains, (truncated) polynomial, and power series rings over \(\mathbb{Q}\)-algebras.
Mathematics Subject Classification ID: 16W70
Mathematics Subject Classification ID: 13F25
zbMATH DE Number: 2171571
zbMATH Keywords: filtered \(\lambda\)-rings
zbMATH Keywords: filtered rings
zbMATH Keywords: power series rings
zbMATH Keywords: ring maps
author: Donald Yau
MaRDI profile type: Publication
arXiv ID: math/0209031
description: scientific article