$R^ {1\vert 1}$-supergroup actions and superdifferential equations
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- by F. Ongay-Larios and O. A. Sánchez-Valenzuela PDF
- Proc. Amer. Math. Soc. 116 (1992), 843-850 Request permission
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 ${{\mathbf {R}}^{1|1}}$ 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 ${{\mathbf {R}}^{1|1}}$-action are given by the Lie superbracket of the field with itself and the Lie bracket of its homogeneous components.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 843-850
- MSC: Primary 58C50; Secondary 22E70, 58A50
- DOI: https://doi.org/10.1090/S0002-9939-1992-1143224-6
- MathSciNet review: 1143224