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2008, preprint arXiv:0808.0785v1 [math.RA] (2008)

Abstract:

Supergroups are introduced in supergeometry via their functor of points. Unlikely the classical, geometric case, the points over a field of a supergroup tell one very little of the supergroup itself: such points miss the odd coordinates and describe only the classical part of the supergroup. This functor of points approach realizes an affine supergroup as a representable group, that is a valued functor from the category of superalgebras (S_alg) to the category of sets (Sets), where superalgebras are just Z_2--graded algebras. Thus, the supergeometric properties were encoded by the category of superalgebras, while the 'supergeometric' functors are valued in ordinary categories of sets, groups, Lie algebras atc, as it is customary in supergeometry. Whereas such a geometric approach is very elegant, one can call it a supergroup one. Key words: supergeometry, transformation supergroups, Chevalley Lie algebra http://www.mat.uniroma2.it/~gavarini/page-web_files/references-data/29-intro.pdf

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http://www.mat.uniroma2.it/~gavarini/page-web_files/references-data/29-intro.pdf Open access

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