Symmetric functions, formal group laws, and Lazard's theorem
type: Item
instance of: scholarly article
title: Symmetric functions, formal group laws, and Lazard's theorem
zbMATH Open document ID: 0934.14030
author: Cristian Lenart
published in: Advances in Mathematics
publication date: 1999-01-26T00:00:00Z
review text: Lazard's theorem is a central result in formal group theory; it states that the ring over which the universal formal group law is defined (known as the Lazard ring) is a polynomial algebra over the integers with infinitely many generators. The author provides a new proof of Lazard's theorem, which is very interesting because it adds new and unexpected insight into the Lazard ring. The main idea is to set up a connection between the Lazard ring and the subalgebra of symmetric functions generated by the monomial symmetric functions indexed by partitions with all parts at least 2, a subalgebra which did not attract any attention so far. In particular, a new set of polynomial generators of the Lazard ring is identified, which is more convenient to work with than previously known ones. These generators are constructed as the images (under the correspondence between symmetric functions and the Lazard ring) of certain linear combinations of forgotten symmetric functions. As application of the results, the construction of a family of \(p\)-typical formal group laws is presented.
Mathematics Subject Classification ID: 14L05
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 55N22
zbMATH DE Number: 1203775
zbMATH Keywords: formal group law
zbMATH Keywords: Lazard ring
zbMATH Keywords: Lazard's theorem
zbMATH Keywords: symmetric functions
reviewed by: C. Krattenthaler
MaRDI profile type: Publication
OpenAlex ID: W2058450538
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DOI: 10.1006/AIMA.1997.1696
description: scientific article; zbMATH DE number 1203775