Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras

Alexey A. Magazev ; Vitaly V. Mikheyev ; Igor V. Shirokov

Symmetry, integrability and geometry: methods and applications, Tome 11 (2015)

Résumé

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.

Détail

Keywords: Lie group; Lie algebra; left- and right-invariant vector fields; composition function; canonical coordinates.

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