Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras
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| Creator |
Agore, A.L.
Militaru, G. |
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| 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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| Date |
2019-02-10T11:26:00Z
2019-02-10T11:26:00Z 2014 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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