Cohomology of Restricted Filiform Lie Algebras mλ₂(p)
For the p-dimensional filiform Lie algebra m₂(p) over a field F of prime characteristic p≥5 with nonzero Lie brackets [e₁,eᵢ]=eᵢ₊₁ for 1 < i < p and [e₂,eᵢ]=eᵢ₊₂ for 2 < i < p − 1, we show that there is a family mλ₂(p) of restricted Lie algebra structures parameterized by...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210293 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Cohomology of Restricted Filiform Lie Algebras mλ₂(p) / T.J. Evans, A. Fialowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 15 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862668217123602432 |
|---|---|
| author | Evans, T.J. Fialowski, A. |
| author_facet | Evans, T.J. Fialowski, A. |
| citation_txt | Cohomology of Restricted Filiform Lie Algebras mλ₂(p) / T.J. Evans, A. Fialowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For the p-dimensional filiform Lie algebra m₂(p) over a field F of prime characteristic p≥5 with nonzero Lie brackets [e₁,eᵢ]=eᵢ₊₁ for 1 < i < p and [e₂,eᵢ]=eᵢ₊₂ for 2 < i < p − 1, we show that there is a family mλ₂(p) of restricted Lie algebra structures parameterized by elements λ ∈ ᵖ. We explicitly describe bases for the ordinary and restricted 1- and 2-cohomology spaces with trivial coefficients, and give formulas for the bracket and [p]-operations in the corresponding restricted one-dimensional central extensions.
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| first_indexed | 2025-12-07T21:25:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210293 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:25:03Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Evans, T.J. Fialowski, A. 2025-12-05T09:23:05Z 2019 Cohomology of Restricted Filiform Lie Algebras mλ₂(p) / T.J. Evans, A. Fialowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 15 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B50; 17B56 arXiv: 1901.07532 https://nasplib.isofts.kiev.ua/handle/123456789/210293 https://doi.org/10.3842/SIGMA.2019.095 For the p-dimensional filiform Lie algebra m₂(p) over a field F of prime characteristic p≥5 with nonzero Lie brackets [e₁,eᵢ]=eᵢ₊₁ for 1 < i < p and [e₂,eᵢ]=eᵢ₊₂ for 2 < i < p − 1, we show that there is a family mλ₂(p) of restricted Lie algebra structures parameterized by elements λ ∈ ᵖ. We explicitly describe bases for the ordinary and restricted 1- and 2-cohomology spaces with trivial coefficients, and give formulas for the bracket and [p]-operations in the corresponding restricted one-dimensional central extensions. The authors are grateful to Dmitry Fuchs for fruitful conversations and the referees whose comments greatly improved the exposition of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Cohomology of Restricted Filiform Lie Algebras mλ₂(p) Article published earlier |
| spellingShingle | Cohomology of Restricted Filiform Lie Algebras mλ₂(p) Evans, T.J. Fialowski, A. |
| title | Cohomology of Restricted Filiform Lie Algebras mλ₂(p) |
| title_full | Cohomology of Restricted Filiform Lie Algebras mλ₂(p) |
| title_fullStr | Cohomology of Restricted Filiform Lie Algebras mλ₂(p) |
| title_full_unstemmed | Cohomology of Restricted Filiform Lie Algebras mλ₂(p) |
| title_short | Cohomology of Restricted Filiform Lie Algebras mλ₂(p) |
| title_sort | cohomology of restricted filiform lie algebras mλ₂(p) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210293 |
| work_keys_str_mv | AT evanstj cohomologyofrestrictedfiliformliealgebrasmλ2p AT fialowskia cohomologyofrestrictedfiliformliealgebrasmλ2p |