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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862683061670379520 |
|---|---|
| author | Agore, A.L. Militaru, G. |
| author_facet | Agore, A.L. Militaru, G. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T15:54:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146642 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:54:54Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Agore, A.L. Militaru, G. 2019-02-10T11:26:00Z 2019-02-10T11:26:00Z 2014 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 https://nasplib.isofts.kiev.ua/handle/123456789/146642 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. We would like to thank the referees for their comments and suggestions that substantially
 improved the first version of this paper. A.L. Agore is research fellow ‘Aspirant’ of FWOVlaanderen.
 This work was supported by a grant of the Romanian National Authority for
 Scientific Research, CNCS-UEFISCDI, grant no. 88/05.10.2011. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras Article published earlier |
| spellingShingle | Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras Agore, A.L. Militaru, G. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146642 |
| work_keys_str_mv | AT agoreal bicrossedproductsmatchedpairdeformationsandthefactorizationindexforliealgebras AT militarug bicrossedproductsmatchedpairdeformationsandthefactorizationindexforliealgebras |