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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The axioms of supermanifolds and a new structure arising from them


Author: Mitchell J. Rothstein
Journal: Trans. Amer. Math. Soc. 297 (1986), 159-180
MSC: Primary 58A50; Secondary 58C50
MathSciNet review: 849473
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Abstract: An analysis of supermanifolds over an arbitrary graded-commmutative algebra is given, proceeding from a set of axioms the first of which is that the derivations of the structure sheaf of a supermanifold are locally free. These axioms are satisfied not by the sheaf of $ {G^\infty }$ functions, as has been asserted elsewhere, but by an extension of this sheaf. A given $ {G^\infty }$ manifold may admit many supermanifold extensions, and it is unknown at present whether there are $ {G^\infty }$ manifolds that admit no such extension. When the underlying graded-commutative algebra is commutative, the axioms reduce to the Berezin-Kostant supermanifold theory.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0849473-8
PII: S 0002-9947(1986)0849473-8
Article copyright: © Copyright 1986 American Mathematical Society