JP Journal of Geometry and Topology
Volume 6, Issue 2, Pages 131 - 135
(July 2006)
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THE MAURER-CARTAN CONNECTION AND A COVARIANT VERSION OF THE LEMMA OF POINCARÉ
José L. Martínez-Morales (Mexico)
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Abstract:
Let a vectorial bundle on a Lie group of matrices, so that for any two intersecting trivializing charts, an element g of the group exists such that the components of the transition functions are (i) right multiplication by g, and (ii) the linear transformation defined by g. Then a connection on the bundle exists such that on each trivializing chart, the forms of the connection are the Maurer-Cartan forms.
In this bundle, a vector-valued form on the group whose covariant derivative on a trivializing chart is zero, is locally “covariantly exact”. |
| Keywords and phrases: vectorial bundle on a Lie group of matrices, intersecting trivializing charts, linear transformation, Maurer-Cartan forms. |
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