A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms
A Lie algebra gQ over Q is said to be R-universal if every homomorphism from gQ to gl(n,R) is conjugate to a homomorphism into gl(n,Q) (for every n). By using Galois cohomology, we provide a short proof of the known fact that every real semisimple Lie algebra has an R-universal Q-form. We also provi...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2015 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147011 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms / D.W. Morris // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862678689475461120 |
|---|---|
| author | Morris, D.W. |
| author_facet | Morris, D.W. |
| citation_txt | A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms / D.W. Morris // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A Lie algebra gQ over Q is said to be R-universal if every homomorphism from gQ to gl(n,R) is conjugate to a homomorphism into gl(n,Q) (for every n). By using Galois cohomology, we provide a short proof of the known fact that every real semisimple Lie algebra has an R-universal Q-form. We also provide a classification of the R-universal Lie algebras that are semisimple.
|
| first_indexed | 2025-12-07T15:41:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147011 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:41:39Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Morris, D.W. 2019-02-12T20:33:33Z 2019-02-12T20:33:33Z 2015 A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms / D.W. Morris // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B10; 17B20; 11E72; 20G30 DOI:10.3842/SIGMA.2015.034 https://nasplib.isofts.kiev.ua/handle/123456789/147011 A Lie algebra gQ over Q is said to be R-universal if every homomorphism from gQ to gl(n,R) is conjugate to a homomorphism into gl(n,Q) (for every n). By using Galois cohomology, we provide a short proof of the known fact that every real semisimple Lie algebra has an R-universal Q-form. We also provide a classification of the R-universal Lie algebras that are semisimple. It is a pleasure to thank V. Chernousov for a very helpful discussion about Tits algebras of special
 orthogonal groups, A. Rapinchuk for explaining how to prove Lemma 2.5, and the anonymous
 referees for numerous very insightful comments on a previous version of this manuscript, including
 some important corrections. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms Article published earlier |
| spellingShingle | A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms Morris, D.W. |
| title | A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms |
| title_full | A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms |
| title_fullStr | A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms |
| title_full_unstemmed | A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms |
| title_short | A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms |
| title_sort | cohomological proof that real representations of semisimple lie algebras have q-forms |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147011 |
| work_keys_str_mv | AT morrisdw acohomologicalproofthatrealrepresentationsofsemisimpleliealgebrashaveqforms AT morrisdw cohomologicalproofthatrealrepresentationsofsemisimpleliealgebrashaveqforms |