The Great Heritage of Sophus Lie

M. Rahula

Tartu University, Estonia

Abstract: In the paper, we describe the floors $T^kM$, sector-bundles, and the theory of sector forms according to J. T. White. Using iterations of the tangent functor $T$, we construct tangent groups $T^kG$. Using the Lie–Cartan calculus, we study invariants of the group operators, their transformations under symmetries and stability.

Keywords: jets, tangent functor, floor, tangent group, stability of invariants.

UDC: 514.7

Received: 27.05.2009