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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Two approaches to supermanifolds


Author: Marjorie Batchelor
Journal: Trans. Amer. Math. Soc. 258 (1980), 257-270
MSC: Primary 58A05; Secondary 81C99
MathSciNet review: 554332
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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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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