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
DOI:
https://doi.org/10.1090/S0002-9947-1986-0849473-8
MathSciNet review:
849473
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Abstract | References | Similar Articles | Additional Information
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 functions, as has been asserted elsewhere, but by an extension of this sheaf. A given
manifold may admit many supermanifold extensions, and it is unknown at present whether there are
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:
https://doi.org/10.1090/S0002-9947-1986-0849473-8
Article copyright:
© Copyright 1986
American Mathematical Society