2 research outputs found
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras
Methods of construction of the composition function, left- and
right-invariant vector fields and differential 1-forms of a Lie group from the
structure constants of the associated Lie algebra are proposed. It is shown
that in the second canonical coordinates these problems are reduced to the
matrix inversions and matrix exponentiations, and the composition function can
be represented in quadratures. Moreover, it is proven that the transition
function from the first canonical coordinates to the second canonical
coordinates can be found by quadratures