Two approaches to supermanifolds
Author:
Marjorie Batchelor
Journal:
Trans. Amer. Math. Soc. 258 (1980), 257-270
MSC:
Primary 58A05; Secondary 81C99
DOI:
https://doi.org/10.1090/S0002-9947-1980-0554332-9
MathSciNet review:
554332
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Abstract | References | Similar Articles | Additional Information
Abstract: The problem of supplying an analogue of a manifold whose sheaf of functions contains anticommuting elements has been approached in two ways. Either one extends the sheaf of functions formally, as in the category of graded manifolds [3], [8], or one mimicks the usual definition of a manifold, having replaced Euclidean space with a suitable product of the odd and even parts of an exterior algebra as in the category of supermanifolds [6]. This paper establishes the equivalence of the category of supermanifolds with the category of graded manifolds.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1980-0554332-9
Keywords:
Supermanifolds,
graded manifolds,
graded Lie algebras,
superspace,
anticommuting coordinates
Article copyright:
© Copyright 1980
American Mathematical Society