Rings of continuous functions, symmetric products, and Frobenius algebras

Details Rings of continuous functions, symmetric products, and Frobenius algebras Rings of continuous functions, symmetric products, and Frobenius algebras

2004-03-22

arxiv.org/abs/math/0403357v1

Mathematics

Rings and Algebras

To appear in Russian Math Surveys

Scientific paper

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.

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