On the asymptotic behaviour of the graded-star-codimension sequence of upper triangular matrices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908170634395648 |
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| author | Diniz, Diogo Yasumura, Felipe Yukihide |
| author_facet | Diniz, Diogo Yasumura, Felipe Yukihide |
| contents | We study the algebra of upper triangular matrices endowed with a group grading and a homogeneous involution over an infinite field. We compute the asymptotic behaviour of its (graded) star-codimension sequence. It turns out that the asymptotic growth of the sequence is independent of the grading and the involution under consideration, depending solely on the size of the matrix algebra. This independence of the group grading also applies to the graded codimension sequence of the associative algebra of upper triangular matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the asymptotic behaviour of the graded-star-codimension sequence of upper triangular matrices Diniz, Diogo Yasumura, Felipe Yukihide Rings and Algebras 16R50 (primary), 16W50 (secondary) We study the algebra of upper triangular matrices endowed with a group grading and a homogeneous involution over an infinite field. We compute the asymptotic behaviour of its (graded) star-codimension sequence. It turns out that the asymptotic growth of the sequence is independent of the grading and the involution under consideration, depending solely on the size of the matrix algebra. This independence of the group grading also applies to the graded codimension sequence of the associative algebra of upper triangular matrices. |
| title | On the asymptotic behaviour of the graded-star-codimension sequence of upper triangular matrices |
| topic | Rings and Algebras 16R50 (primary), 16W50 (secondary) |
| url | https://arxiv.org/abs/2408.00087 |