Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147137 |
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| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Magazev, A.A. Mikheyev, V.V. Shirokov, I.V. 2019-02-13T17:21:00Z 2019-02-13T17:21:00Z 2015 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. 1815-0659 2010 Mathematics Subject Classification: 22E05; 22E60; 22E70 DOI:10.3842/SIGMA.2015.066 https://nasplib.isofts.kiev.ua/handle/123456789/147137 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. 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). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras |
| spellingShingle |
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras Magazev, A.A. Mikheyev, V.V. Shirokov, I.V. |
| title_short |
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras |
| title_full |
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras |
| title_fullStr |
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras |
| title_full_unstemmed |
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras |
| title_sort |
computation of composition functions and invariant vector fields in terms of structure constants of associated lie algebras |
| author |
Magazev, A.A. Mikheyev, V.V. Shirokov, I.V. |
| author_facet |
Magazev, A.A. Mikheyev, V.V. Shirokov, I.V. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147137 |
| citation_txt |
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. |
| work_keys_str_mv |
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| first_indexed |
2025-12-07T20:08:51Z |
| last_indexed |
2025-12-07T20:08:51Z |
| _version_ |
1850881481008742400 |