Certain invariants of generic matrix algebras
Let \(K\) be a field of characteristic zero, \(W\) be the associative unital algebra generated by two generic traceless matrices \(X,\) \(Y.\) We also handle the Lie subalgebra \(L\) of the algebra \(W\) consisting of its Lie elements. Consider the subgroup \(G=\langle e_{21}-e_{12}\rangle\) of the...
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| Date: | 2024 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2024
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2195 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543251282001920 |
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| author | Öğüşlü, Nazar Ş. Fındık, Şehmus |
| author_facet | Öğüşlü, Nazar Ş. Fındık, Şehmus |
| author_sort | Öğüşlü, Nazar Ş. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2024-09-23T09:29:11Z |
| description | Let \(K\) be a field of characteristic zero, \(W\) be the associative unital algebra generated by two generic traceless matrices \(X,\) \(Y.\) We also handle the Lie subalgebra \(L\) of the algebra \(W\) consisting of its Lie elements. Consider the subgroup \(G=\langle e_{21}-e_{12}\rangle\) of the special linear group \(SL_2(K)\) of order 4. In this study, we give free generators of the algebras \(W^G\) and \(L^G\) of invariants of the group \(G\) as a \(C(W)^G\)-module. |
| first_indexed | 2025-12-02T15:31:06Z |
| format | Article |
| id | admjournalluguniveduua-article-2195 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:31:06Z |
| publishDate | 2024 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-21952024-09-23T09:29:11Z Certain invariants of generic matrix algebras Öğüşlü, Nazar Ş. Fındık, Şehmus generic, invariant, Lie algebra 13A50, 16R30, 17B01 Let \(K\) be a field of characteristic zero, \(W\) be the associative unital algebra generated by two generic traceless matrices \(X,\) \(Y.\) We also handle the Lie subalgebra \(L\) of the algebra \(W\) consisting of its Lie elements. Consider the subgroup \(G=\langle e_{21}-e_{12}\rangle\) of the special linear group \(SL_2(K)\) of order 4. In this study, we give free generators of the algebras \(W^G\) and \(L^G\) of invariants of the group \(G\) as a \(C(W)^G\)-module. Lugansk National Taras Shevchenko University 2024-09-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2195 10.12958/adm2195 Algebra and Discrete Mathematics; Vol 38, No 1 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2195/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2195/1144 Copyright (c) 2024 Algebra and Discrete Mathematics |
| spellingShingle | generic invariant Lie algebra 13A50 16R30 17B01 Öğüşlü, Nazar Ş. Fındık, Şehmus Certain invariants of generic matrix algebras |
| title | Certain invariants of generic matrix algebras |
| title_full | Certain invariants of generic matrix algebras |
| title_fullStr | Certain invariants of generic matrix algebras |
| title_full_unstemmed | Certain invariants of generic matrix algebras |
| title_short | Certain invariants of generic matrix algebras |
| title_sort | certain invariants of generic matrix algebras |
| topic | generic invariant Lie algebra 13A50 16R30 17B01 |
| topic_facet | generic invariant Lie algebra 13A50 16R30 17B01 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2195 |
| work_keys_str_mv | AT oguslunazars certaininvariantsofgenericmatrixalgebras AT fındıksehmus certaininvariantsofgenericmatrixalgebras |