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

Abstract

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.

References in corpus (1)

• Faithful representations of Lie algebras and Homogeneous Spaces

Cited by in corpus (5)

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• Noncommutative integration of the Dirac equation in homogeneous spaces
• Classification of scalar second-order differential equations with low-dimensional symmetry groups: The case of free action