The Gelfand map and symmetric products
Combinatorics
2007-05-23 v1 Algebraic Geometry
Functional Analysis
Abstract
If A is an algebra of functions on X, there are many cases when X can be regarded as included in Hom(A,C) as the set of ring homomorphisms. In this paper the corresponding results for the symmetric products of X are introduced. It is shown that the symmetric product Sym^n(X) is included in Hom(A,C) as the set of those functions that satisfy equations generalising f(xy)=f(x)f(y). These equations are related to formulae introduced by Frobenius and, for the relevant A, they characterise linear maps on A that are the sum of ring homomorphisms. The main theorem is proved using an identity satisfied by partitions of finite sets.
Cite
@article{arxiv.math/0109122,
title = {The Gelfand map and symmetric products},
author = {V. M. Buchstaber and E. G. Rees},
journal= {arXiv preprint arXiv:math/0109122},
year = {2007}
}
Comments
14 pages, Latex