Graded manifolds,supermanifolds and infinite-dimensional Grassmann algebras |
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Authors: | Alice Rogers |
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Institution: | (1) Department of Mathematics, King's College, Strand, WC2 London, England |
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Abstract: | A new approach to superdifferentiable functions of Grassmann variables is developed, which avoids ambiguities in odd derivatives. This is used to give an improved definition of supermanifold over a finite-dimensional Grassmann algebra. A natural embedding of super-manifolds over Grassmann algebras with increasing number (L) of generators is developed, and thus a limit asL tends to infinity is possible. A correspondence between graded manifolds and supermanifolds is constructed, extending results of 5] and 8].Research supported by the SERC under advanced research fellowship number B/AF/687 |
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