The Gelfand map and symmetric products
The Gelfand map and symmetric products
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Gelfand 映射和对称积
DOI：
10.1007/pl00012597
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
E. Rees
中科院分区：
文献类型：
--
作者：
V. Buchstaber;E. Rees
如果A是X上的函数代数，则在许多情况下，X可以被视为包含在HOM(A，C)中的环同态集。本文介绍了关于X的对称乘积的相应结果。证明了对称乘积Sym^n(X)包含在Hom(A，C)中，作为满足广义方程f(Xy)=f(X)f(Y)的函数集.这些方程与Frobenius提出的公式有关，并且对于相关的A，它们刻画了A上的线性映射，这些映射是环同态的和。利用有限集的划分所满足的恒等式证明了主要定理。
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.