Rings of continuous functions, symmetric products, and Frobenius algebras

Abstract

Properties of higher characters are developed and applied to symmetric products and Frobenius algebras. A `constructive' proof of the Gel'fand-Kolmogorov theorem is given. Generalisations of that theorem and the Nullstellensatz to symmetric products are discussed.Applications to the theory of multi-symmetric functions are also discussed. It is proved that the first three characters determine the Jordan algebra associated to a Frobenius algebra and as a corollary one obtains the theorem of Hoehnke and Johnson that a finite group is determined by the first three characters of its regular representation.

To appear in Russian Math Surveys

Cited by in corpus (5)

• Vector invariants of a class of pseudo-reflection groups and multisymmetric syzygies
• A short proof of the Buchstaber-Rees theorem
• Fricke identities, Frobenius $k$-characters and Markov equation
• On the Buchstaber--Rees theory of "Frobenius $n$-homomorphisms" and its generalization
• On generalized symmetric powers and a generalization of Kolmogorov-Gelfand-Buchstaber-Rees theory