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arXiv · 0709.4402

Operators on superspaces and generalizations of the Gelfand-Kolmogorov theorem

H. M. Khudaverdian·Th. Th. Voronov
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Abstract

(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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H. M. Khudaverdian, Th. Th. Voronov. 2007-09-27. Operators on superspaces and generalizations of the Gelfand-Kolmogorov theorem. https://doi.org/10.1063/1.2820962

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