Symmetric functions, formal group laws, and Lazard's theorem
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.
scientific article; zbMATH DE number 1203775
scientific article