XXVI Workshop on Geometric Methods in Physics 1-7.07.2007

Theodore Voronov

Operators on superspace and generalizations of the Gelfand-Kolomogorov theorem

Gelfand and Kolmogorov in 1939 proved that any compact Hausdorff space X is embedded into the infinite-dimensional vector space C(X)^* (the dual space to the algebra of continuous functions C(X)) as an "algebraic variety", in a certain sense. Buchstaber and Rees have recently extended this to the symmetric powers Sym^n(X). We give a simplification and a further extension of this theory based, rather unexpectedly, on results from super linear algebra. See arXiv:math.RA/0612072. (Joint work with H. Khudaverdian.)