The Gelfand map and symmetric products

Details The Gelfand map and symmetric products The Gelfand map and symmetric products

2001-09-18

arxiv.org/abs/math/0109122v1

Mathematics

Combinatorics

14 pages, Latex

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Gelfand map and symmetric products does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Gelfand map and symmetric products, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Gelfand map and symmetric products will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-425111