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The discrete Gelfand transform and its dual

V. Buchstaber·A. Lazarev
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Abstract

We consider the transformation $\ev$ which associates to any element in a K-algebra A a function on the the set of its K-points. This is the analogue of the fundamental Gelfand transform. Both $\ev$ and its dual $\ev^*$ are the maps from a discrete K-module to a topological K-module and we investigate in which case the image of each map is dense. The answer is nontrivial for various choices of K and A already for A=K[x], the polynomial ring in one variable. Applications to the structure of algebras of cohomology operations are given.

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V. Buchstaber, A. Lazarev. 2004-04-26. The discrete Gelfand transform and its dual. https://arxiv.org/abs/math/0404443

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