Operators on superspaces and generalizations of the Gelfand-Kolmogorov theorem

Details Operators on superspaces and generalizations of the Gelfand-Kolmogorov theorem Operators on superspaces and generalizations of the Gelfand-Kolmogorov theorem

2007-09-27

arxiv.org/abs/0709.4402v1

Physics

Mathematical Physics

LaTeX, 7 pages. Based on a talk at the Bialowieza meeting, July 2007

Scientific paper

10.1063/1.2820962

(Write-up of a talk at the Bialowieza meeting, July 2007.) Gelfand and Kolmogorov in 1939 proved that a compact Hausdorff topological space $X$ can be canonically embedded into the infinite-dimensional vector space $C(X)^* $, the dual space of the algebra of continuous functions $C(X)$ as an "algebraic variety" specified by an infinite system of quadratic equations. Buchstaber and Rees have recently extended this to all symmetric powers $\Sym^n(X)$ using their notion of the Frobenius $n$-homomorphisms. We give a simplification and a further extension of this theory, which is based, rather unexpectedly, on results from super linear lgebra.

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