Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras
For a perfect Lie algebra h we classify all Lie algebras containing h as a subalgebra of codimension 1. The automorphism groups of such Lie algebras are fully determined as subgroups of the semidirect product h⋉(k∗×AutLie(h)). In the non-perfect case the classification of these Lie algebras is a dif...
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| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146642 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras / A.L. Agore, G. Militaru // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 22 назв. — англ. |
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irk-123456789-1466422019-02-11T01:23:45Z Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras Agore, A.L. Militaru, G. For a perfect Lie algebra h we classify all Lie algebras containing h as a subalgebra of codimension 1. The automorphism groups of such Lie algebras are fully determined as subgroups of the semidirect product h⋉(k∗×AutLie(h)). In the non-perfect case the classification of these Lie algebras is a difficult task. Let l(2n+1,k) be the Lie algebra with the bracket [Ei,G]=Ei, [G,Fi]=Fi, for all i=1,…,n. We explicitly describe all Lie algebras containing l(2n+1,k) as a subalgebra of codimension 1 by computing all possible bicrossed products k⋈l(2n+1,k). They are parameterized by a set of matrices Mn(k)⁴×k²ⁿ⁺² which are explicitly determined. Several matched pair deformations of l(2n+1,k) are described in order to compute the factorization index of some extensions of the type k⊂k⋈l(2n+1,k). We provide an example of such extension having an infinite factorization index. 2014 Article Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras / A.L. Agore, G. Militaru // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B05; 17B55; 17B56 DOI:10.3842/SIGMA.2014.065 http://dspace.nbuv.gov.ua/handle/123456789/146642 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 |
For a perfect Lie algebra h we classify all Lie algebras containing h as a subalgebra of codimension 1. The automorphism groups of such Lie algebras are fully determined as subgroups of the semidirect product h⋉(k∗×AutLie(h)). In the non-perfect case the classification of these Lie algebras is a difficult task. Let l(2n+1,k) be the Lie algebra with the bracket [Ei,G]=Ei, [G,Fi]=Fi, for all i=1,…,n. We explicitly describe all Lie algebras containing l(2n+1,k) as a subalgebra of codimension 1 by computing all possible bicrossed products k⋈l(2n+1,k). They are parameterized by a set of matrices Mn(k)⁴×k²ⁿ⁺² which are explicitly determined. Several matched pair deformations of l(2n+1,k) are described in order to compute the factorization index of some extensions of the type k⊂k⋈l(2n+1,k). We provide an example of such extension having an infinite factorization index. |
| format |
Article |
| author |
Agore, A.L. Militaru, G. |
| spellingShingle |
Agore, A.L. Militaru, G. Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Agore, A.L. Militaru, G. |
| author_sort |
Agore, A.L. |
| title |
Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras |
| title_short |
Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras |
| title_full |
Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras |
| title_fullStr |
Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras |
| title_full_unstemmed |
Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras |
| title_sort |
bicrossed products, matched pair deformations and the factorization index for lie algebras |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146642 |
| citation_txt |
Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras / A.L. Agore, G. Militaru // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 22 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT agoreal bicrossedproductsmatchedpairdeformationsandthefactorizationindexforliealgebras AT militarug bicrossedproductsmatchedpairdeformationsandthefactorizationindexforliealgebras |
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2023-05-20T17:25:19Z |
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2023-05-20T17:25:19Z |
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