Аннотация:
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.
Образец цитирования:
Alexey A. Magazev, Vitaly V. Mikheyev, Igor V. Shirokov, “Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras”, SIGMA, 11 (2015), 066, 17 pp.
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\by Alexey~A.~Magazev, Vitaly~V.~Mikheyev, Igor~V.~Shirokov
\paper Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras
\jour SIGMA
\yr 2015
\vol 11
\papernumber 066
\totalpages 17
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\crossref{https://doi.org/10.3842/SIGMA.2015.066}
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https://www.mathnet.ru/rus/sigma1047
https://www.mathnet.ru/rus/sigma/v11/p66
Эта публикация цитируется в следующих 9 статьяx:
О. Л. Курнявко, И. В. Широков, “Построение инвариантных дифференциальных операторов первого порядка”, Изв. вузов. Матем., 2024, № 5, 37–46 [O. L. Kurnyavko, I. V. Shirokov, “Construction of first-order invariant differential operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 5, 37–46]
O. L. Kurnyavko, I. V. Shirokov, “Construction of First-Order Invariant Differential Operators”, Russ Math., 68:5 (2024), 27
A. A. Magazev, I. V. Shirokov, “The Structure of Differential Invariants for a Free Symmetry Group Action”, Russ Math., 67:6 (2023), 26
Magazev A.A., “Constructing a Complete Integral of the Hamilton-Jacobi Equation on Pseudo-Riemannian Spaces With Simply Transitive Groups of Motions”, Math. Phys. Anal. Geom., 24:2 (2021), 11
Katarzyna Grabowska, Janusz Grabowski, “Solvable Lie Algebras of Vector Fields and a Lie's Conjecture”, SIGMA, 16 (2020), 065, 14 pp.
A. Breev, A. Shapovalov, “Non-commutative integration of the Dirac equation in homogeneous spaces”, Symmetry-Basel, 12:11 (2020), 1867
D. A. Ivanov, A. I. Breev, “Noncommutative reduction of the Bloch equation in the Heisenberg-Weyl group”, Russ. Phys. J., 61:3 (2018), 556–565
M. Nesterenko, S. Posta, “Comparison of realizations of Lie algebras”, XXV International Conference on Integrable Systems and Quantum Symmetries (ISQS-25), Journal of Physics Conference Series, 965, IOP Publishing Ltd, 2018, UNSP 012028
Nesterenko M., Posta S., Vaneeva O., “Realizations of Galilei Algebras”, J. Phys. A-Math. Theor., 49:11 (2016), 115203
Цитирование в формате AMSBIB
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