Universal property of skew PBW extensions
In this paper we prove the universal property of skew $PBW$ extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew $PBW$ extensions include as particular examp...
Збережено в:
| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2015 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/154757 |
| 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: | Universal property of skew PBW extensions / J,.P. Acosta, O. Lezama // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 1. — С. 1-12 . — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862660865748107264 |
|---|---|
| author | Acosta, J,.P. Lezama, O. |
| author_facet | Acosta, J,.P. Lezama, O. |
| citation_txt | Universal property of skew PBW extensions / J,.P. Acosta, O. Lezama // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 1. — С. 1-12 . — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | In this paper we prove the universal property of skew $PBW$ extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew $PBW$ extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials, diffusion algebras, Manin algebra of quantum matrices, among many others. As a corollary we will give a new short proof of the Poincar\'{e}-Birkhoff-Witt theorem about the bases of enveloping algebras of finite-dimensional Lie algebras.
|
| first_indexed | 2025-12-02T11:38:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154757 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-02T11:38:04Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Acosta, J,.P. Lezama, O. 2019-06-15T20:00:54Z 2019-06-15T20:00:54Z 2015 Universal property of skew PBW extensions / J,.P. Acosta, O. Lezama // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 1. — С. 1-12 . — Бібліогр.: 10 назв. — англ. 1726-3255 2010 MSC:Primary: 16S10, 16S80; Secondary: 16S30, 16S36. https://nasplib.isofts.kiev.ua/handle/123456789/154757 In this paper we prove the universal property of skew $PBW$ extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew $PBW$ extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials, diffusion algebras, Manin algebra of quantum matrices, among many others. As a corollary we will give a new short proof of the Poincar\'{e}-Birkhoff-Witt theorem about the bases of enveloping algebras of finite-dimensional Lie algebras. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Universal property of skew PBW extensions Article published earlier |
| spellingShingle | Universal property of skew PBW extensions Acosta, J,.P. Lezama, O. |
| title | Universal property of skew PBW extensions |
| title_full | Universal property of skew PBW extensions |
| title_fullStr | Universal property of skew PBW extensions |
| title_full_unstemmed | Universal property of skew PBW extensions |
| title_short | Universal property of skew PBW extensions |
| title_sort | universal property of skew pbw extensions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154757 |
| work_keys_str_mv | AT acostajp universalpropertyofskewpbwextensions AT lezamao universalpropertyofskewpbwextensions |