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$ R\sp {1\vert 1}$-supergroup actions and superdifferential equations

Authors: F. Ongay-Larios and O. A. Sánchez-Valenzuela
Journal: Proc. Amer. Math. Soc. 116 (1992), 843-850
MSC: Primary 58C50; Secondary 22E70, 58A50
MathSciNet review: 1143224
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Abstract: The problem of posing and solving ordinary differential equations on supermanifolds is addressed from the point of view of Lie's theory. It is shown that no nonsingular, nondegenerate, odd supervector field can have a Lie supergroup action of $ {{\mathbf{R}}^{1\vert 1}}$ as its flow. It is also shown that the class of integrable supervector fields goes far beyond homogeneity and rectifiability. The obstructions for the integral flow to be an $ {{\mathbf{R}}^{1\vert 1}}$-action are given by the Lie superbracket of the field with itself and the Lie bracket of its homogeneous components.

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Keywords: Supermanifolds, superdifferential equations, Lie supergroup actions
Article copyright: © Copyright 1992 American Mathematical Society

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