Moduli space of filtered λ-ringstructures over a filtered ring
Motivated in part by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered λ-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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204304138 |
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| Summary: | Motivated in part by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered λ-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 ℤ and 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 λ-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 λ-ring structures over some filtered rings, including rings of dual numbers over binomial domains, (truncated) polynomial, and power series rings over ℚ-algebras. |
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| ISSN: | 0161-1712 1687-0425 |