The discrete Gelfand transform and its dual

VM Buchstaber, A Lazarev

Research output: Contribution to journalArticle (Academic Journal)peer-review


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.
Translated title of the contributionThe discrete Gelfand transform and its dual
Original languageEnglish
Pages (from-to)184 - 186
JournalUspekhi Matematicheskikh Nauk (Russian Mathematical Journal)
Volume59 (1)
Publication statusPublished - Apr 2004

Bibliographical note

Publisher: London Mathematical Society/Turpion Ltd/Russian Academy of Sciences


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