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Graded manifolds, supermanifolds and infinite-dimensional Grassmann algebras

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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].

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Authors and Affiliations

  1. Department of Mathematics, King's College, Strand, WC2, London, England

    Alice Rogers

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  1. Alice Rogers
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Communicated by R. Haag

Research supported by the SERC under advanced research fellowship number B/AF/687

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Rogers, A. Graded manifolds, supermanifolds and infinite-dimensional Grassmann algebras. Commun.Math. Phys. 105, 375–384 (1986). https://doi.org/10.1007/BF01205932

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  • DOI: https://doi.org/10.1007/BF01205932

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