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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| Дата: | 2015 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147137 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147137 |
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irk-123456789-1471372019-02-14T01:25:16Z 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. 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. 2015 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147137 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Magazev, A.A. Mikheyev, V.V. Shirokov, I.V. |
| spellingShingle |
Magazev, A.A. Mikheyev, V.V. Shirokov, I.V. Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Magazev, A.A. Mikheyev, V.V. Shirokov, I.V. |
| author_sort |
Magazev, A.A. |
| title |
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT magazevaa computationofcompositionfunctionsandinvariantvectorfieldsintermsofstructureconstantsofassociatedliealgebras AT mikheyevvv computationofcompositionfunctionsandinvariantvectorfieldsintermsofstructureconstantsofassociatedliealgebras AT shirokoviv computationofcompositionfunctionsandinvariantvectorfieldsintermsofstructureconstantsofassociatedliealgebras |
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2023-05-20T17:26:41Z |
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2023-05-20T17:26:41Z |
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