On infinitesimal transformations of Weil bundles as solutions of differential equation for Lie derivative of complete lift connection

Abstract

Background. The study of infinitesimal affine transformation of bundles over Weil algebra is one of the important problems in the theory of these bundles. Alternative representations of infinitesimal affine transformations of Weil bundle with complete lift connection over special Weil algebra are obtained. Matherials and methods. Methods of tensor analysis and Lie derivative are used. Results. Alternative expressions of infinitesimal affine transformations are obtained, as well as conditions imposed on the components of these transformations. Conclusions. It is proved that infinitesimal affine transformations of Weil bundles with the complete lift connection over special Weil algebras can be represented as a sum of lifts of horizontal and horizontal vector type.

Keywords

• alternative representation
• infinitesimal affine transformation
• weil bundle
• complete lift connection