arXiv subjects

E. G. Rees

Publications and source records attributed to E. G. Rees.

3 recordsLinked to original sources

arXiv2006

Frobenius $n$-homomorphisms, transfers and branched coverings

The main purpose is to characterise continuous maps that are $n$-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius $n$-homomorphisms between two function spaces that correspond to $n$-branched coverings are determined completely. Several equivalent definitions of a Frobenius $n$-homomorphism are compared and some of their properties are proved. An axiomatic treatment of $n$-transfers is given in general and properties of $n$-branched coverings are studied and compared with those of regular coverings.

math.RA↗

arXiv2004

Rings of continuous functions, symmetric products, and Frobenius algebras

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.

math.RA↗

arXiv2001

The Gelfand map and symmetric products

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.

math.CO↗