2013/12/31 by А. А. Магазев, Alexey A. Magazev, Vitaly V. Mikheyev +3 · 11 citations
Mathematics · Physics and Astronomy · #Adjoint representation of a Lie algebra #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algorithm #Composition (language) #Computation #Geometry #Invariant (physics) #Lie algebra #Lie conformal algebra #Lie group #Linguistics #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Philosophy #Pure mathematics #Representation of a Lie group #Structure constants #Vector field #math-ph #math.MP
paper · pdf · doi:10.3842/sigma.2015.066
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)
arxiv created 2015/08/06 · openalex publication_date 2015/08/06 · arxiv updated 2015/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.