The diamond lemma
Spa: The Diamond Lemma provides a general method in order to prove that certain sets are bases of algebras which are defined in terms of generators and relations. For instance, the Poincar´e-Birkhoff-Witt theorem for enveloping algebras can be derived from it. We present some examples that illustrat...
| Main Author: | |
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| Format: | Documento de Conferencia |
| Language: | spa |
| Published: |
2021
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| Online Access: | http://repositorio.uptc.edu.co/handle/001/7824 |
| _version_ | 1801705873731485696 |
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| author | Reyes Villamil, Milton Armando |
| author_facet | Reyes Villamil, Milton Armando |
| author_sort | Reyes Villamil, Milton Armando |
| collection | DSpace |
| description | Spa: The Diamond Lemma provides a general method in order to prove that certain sets are bases of algebras which are defined in terms of generators and relations. For instance, the Poincar´e-Birkhoff-Witt theorem for enveloping algebras can be derived from it. We present some examples that illustrate the usefulness of this lemma. These examples are of interest for modern mathematical physics. The classes of rings we consider include as a special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra of the Lie algebra and others. Key words: Poincaré-Birkhoff-Witt theorem, monomials, generators. |
| format | Documento de Conferencia |
| id | repositorio.uptc.edu.co-001-7824 |
| institution | Repositorio Institucional UPTC |
| language | spa |
| publishDate | 2021 |
| record_format | dspace |
| spelling | repositorio.uptc.edu.co-001-78242022-09-06T16:33:40Z The diamond lemma Reyes Villamil, Milton Armando Spa: The Diamond Lemma provides a general method in order to prove that certain sets are bases of algebras which are defined in terms of generators and relations. For instance, the Poincar´e-Birkhoff-Witt theorem for enveloping algebras can be derived from it. We present some examples that illustrate the usefulness of this lemma. These examples are of interest for modern mathematical physics. The classes of rings we consider include as a special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra of the Lie algebra and others. Key words: Poincaré-Birkhoff-Witt theorem, monomials, generators. 2021-12-21T19:50:00Z 2021-12-21T19:50:00Z 2015-05-02 Documento de Conferencia http://purl.org/coar/resource_type/c_8544 info:eu-repo/semantics/conferenceObject info:eu-repo/semantics/publishedVersion Text http://purl.org/coar/version/c_970fb48d4fbd8a85 http://repositorio.uptc.edu.co/handle/001/7824 830 instname:Universidad Pedagogica y Tecnologica de Colombia reponame:Repositorio de la Universidad Pedagogica y Tecnologica de Colombia repourl:https://repositorio.uptc.edu.co/ spa I Encuentro Internacional de Matemáticas, Estadística y Educación Matemática XXII Jornada de Matemáticas y Estadista https://rdigitales.uptc.edu.co/memorias/index.php/mate_estadistica/mate_estadistica/paper/download/830/821 https://creativecommons.org/licenses/by-nc-sa/4.0/ info:eu-repo/semantics/openAccess Atribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0) http://purl.org/coar/access_right/c_14cb application/pdf application/pdf https://rdigitales.uptc.edu.co/memorias/index.php/mate_estadistica/mate_estadistica/paper/view/830 |
| spellingShingle | Reyes Villamil, Milton Armando The diamond lemma |
| title | The diamond lemma |
| title_full | The diamond lemma |
| title_fullStr | The diamond lemma |
| title_full_unstemmed | The diamond lemma |
| title_short | The diamond lemma |
| title_sort | diamond lemma |
| url | http://repositorio.uptc.edu.co/handle/001/7824 |
| work_keys_str_mv | AT reyesvillamilmiltonarmando thediamondlemma AT reyesvillamilmiltonarmando diamondlemma |
