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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/785| Existence and Uniqueness of Solution to Superdifferential Equations | |
| OSCAR ADOLFO SANCHEZ VALENZUELA | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Ecuaciones Supediferenciales | |
| We state and.prove the theorem of existence and uniqueness of solutions to ordinary superdifferential equations on supermanifolds. It is shown that any supei'vector. field, X= Xo+Xt, ii~ a unique integral flow, r.: JR111 X (M,AM)--+ (M,AM), satisfying a given initial condition. A necessary and sufficient condition for this integral flow to yield an R111-action is obtained: the homogeneous components, Xo, and, X1, of the given field must define a Lie superalgebra of dimension (1, 1). The supergroup structure on JR111 however, has to be specified: there are three non-isomorphic Lie supergroup structures on R111 , all of which have addition as the group operation in the underlying Lie group R. On the other extreme, even if Xo, and X1 do not close to form a Lie superalgebra, the integral flow of X is uniquely determined arid is independent of the Lie ·supergroup structure imposed on JR111 . This fact makes it possible to establish an unambiguous relationship between the algebraic Lie deri'vative of supergeometric obJ~cts (e.g., superforms), and its geometrical definition in terms of integral flows. It is shown by means of examples that if a supergroup structure in R111 is fixed, some flows obtained from left-invariant supervector fields on Lie supergroups may fail to define an R111-action of the choa~n struc.ture. Finally, necessary and sufficient conditions for the integral flows of two supervector fields to commute are given. | |
| Centro de Investigación en Matemáticas | |
| 10-09-1992 | |
| Reporte | |
| Inglés | |
| Investigadores | |
| OTRAS | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Reportes Técnicos - Matemáticas |
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| I-92-07.pdf | 1.32 MB | Adobe PDF | Visualizar/Abrir |