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Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras
Інший ID:
2010 Mathematics Subject Classification: 22E05; 22E60; 22E70
DOI:10.3842/SIGMA.2015.066
DOI:10.3842/SIGMA.2015.066
Посилання:
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras / A.A. Magazev, V.V. Mikheyev, I.V. Shirokov // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 26 назв. — англ.
Підтримка:
ments
Authors greatly appreciate the cooperation of the editors and referees who put decent ef fort and
amount of time to improve the content and style of the paper. We also want to especially thank
the referees for the helpful discussions on the subject of the paper which moved our understanding
of the problem much further. This work was supported by the Ministry of Education and Science
of the Russian Federation (Project no. 3107).
Дата:
2015
Переглядів:
577
Завантажень:
248
Анотація:
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.
