Graded polynomial identities of the infinite-dimensional upper triangular matrices over an arbitrary field
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914681968394240 |
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| author | Garcia, Micael Said Yasumura, Felipe Yukihide |
| author_facet | Garcia, Micael Said Yasumura, Felipe Yukihide |
| contents | We compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis. We find conditions under which a grading on such an algebra satisfies a nontrivial graded polynomial identity. Finally, we provide examples showing that two nonisomorphic gradings can have the same set of graded polynomial identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10839 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graded polynomial identities of the infinite-dimensional upper triangular matrices over an arbitrary field Garcia, Micael Said Yasumura, Felipe Yukihide Rings and Algebras We compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis. We find conditions under which a grading on such an algebra satisfies a nontrivial graded polynomial identity. Finally, we provide examples showing that two nonisomorphic gradings can have the same set of graded polynomial identities. |
| title | Graded polynomial identities of the infinite-dimensional upper triangular matrices over an arbitrary field |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2402.10839 |