Inner automorphisms of Lie algebras related with generic 2 × 2 matrices
Let Fm = Fm(var(sl₂(K))) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl₂(K) over a field K of characteristic 0. Translating an old result of Baker from 1901 we present a multiplication rule for the inner automorphisms of the completion Fmˆ of Fm w...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2012 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/152228 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Inner automorphisms of Lie algebras related with generic 2 × 2 matrices / V. Drensky, S. Fındık // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 49-70. — Бібліогр.: 23 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862576867406512128 |
|---|---|
| author | Drensky, V. Fındık, S. |
| author_facet | Drensky, V. Fındık, S. |
| citation_txt | Inner automorphisms of Lie algebras related with generic 2 × 2 matrices / V. Drensky, S. Fındık // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 49-70. — Бібліогр.: 23 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let Fm = Fm(var(sl₂(K))) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl₂(K) over a field K of characteristic 0. Translating an old result of Baker from 1901 we present a multiplication rule for the inner automorphisms of the completion Fmˆ of Fm with respect to the formal power series topology. Our results are more precise for m = 2 when F₂ is isomorphic to the Lie algebra L generated by two generic traceless 2×2 matrices. We give a complete description of the group of inner automorphisms of Lˆ. As a consequence we obtain similar results for the automorphisms of the relatively free algebra Fm / Fm c⁺¹ = Fm(var(sl₂(K)) ∩ Nc)
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| first_indexed | 2025-11-26T14:36:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152228 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-26T14:36:54Z |
| publishDate | 2012 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Drensky, V. Fındık, S. 2019-06-09T05:50:12Z 2019-06-09T05:50:12Z 2012 Inner automorphisms of Lie algebras related with generic 2 × 2 matrices / V. Drensky, S. Fındık // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 49-70. — Бібліогр.: 23 назв. — англ. 1726-3255 2010 MSC:17B01, 17B30, 17B40, 16R30. https://nasplib.isofts.kiev.ua/handle/123456789/152228 Let Fm = Fm(var(sl₂(K))) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl₂(K) over a field K of characteristic 0. Translating an old result of Baker from 1901 we present a multiplication rule for the inner automorphisms of the completion Fmˆ of Fm with respect to the formal power series topology. Our results are more precise for m = 2 when F₂ is isomorphic to the Lie algebra L generated by two generic traceless 2×2 matrices. We give a complete description of the group of inner automorphisms of Lˆ. As a consequence we obtain similar results for the automorphisms of the relatively free algebra Fm / Fm c⁺¹ = Fm(var(sl₂(K)) ∩ Nc) The research of the first author was partially supported by Grant for Bilateral Scientific Cooperation between Bulgaria and Ukraine. The research of the second author was partially supported by the Council of Higher Education (YÖK) in Turkey. The second named author is grateful to the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences for the creative atmosphere and the warm hospitality during his visit when most of this project was carried out. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Inner automorphisms of Lie algebras related with generic 2 × 2 matrices Article published earlier |
| spellingShingle | Inner automorphisms of Lie algebras related with generic 2 × 2 matrices Drensky, V. Fındık, S. |
| title | Inner automorphisms of Lie algebras related with generic 2 × 2 matrices |
| title_full | Inner automorphisms of Lie algebras related with generic 2 × 2 matrices |
| title_fullStr | Inner automorphisms of Lie algebras related with generic 2 × 2 matrices |
| title_full_unstemmed | Inner automorphisms of Lie algebras related with generic 2 × 2 matrices |
| title_short | Inner automorphisms of Lie algebras related with generic 2 × 2 matrices |
| title_sort | inner automorphisms of lie algebras related with generic 2 × 2 matrices |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152228 |
| work_keys_str_mv | AT drenskyv innerautomorphismsofliealgebrasrelatedwithgeneric22matrices AT fındıks innerautomorphismsofliealgebrasrelatedwithgeneric22matrices |