Tangent and tensor bundles of $(2,0)$ type under Lie group

In the E. V. Nazarova's work the tangent bundle of $TG$ Lie group was studied from the natural and synectics extension point of view of this group in algebra of dual numbers. Invariant synectics linkages under group $G$. Our aim was to study the tangent and tensor bundles $T^2_0G$ under Lie group. These bundles were proved to be trivial and the bundle spaces were proved to be Lie groups. The lifts of these left-invariant vector fields were built un these bundles. Lie algebra of $TG$ group and Lie algebra of $T^2_0G$ under Lie group were found, and the equations of these algebras were obtained. The tangent and $(2,0)$ tensor bundles under 2-dimensional linked Lie groups were regarded as examples.