On star-homogeneous-graded polynomial identities of upper triangular matrices over an arbitrary field
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910318657011712 |
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| author | de Mello, Thiago Castilho Yasumura, Felipe Yukihide |
| author_facet | de Mello, Thiago Castilho Yasumura, Felipe Yukihide |
| contents | We study the graded polynomial identities with a homogeneous involution on the algebra of upper triangular matrices endowed with a fine group grading. We compute their polynomial identities and a basis of the relatively free algebra, considering an arbitrary base field. We obtain the asymptotic behaviour of the codimension sequence when the characteristic of the base field is zero. As a consequence, we compute the exponent and the second exponent of the same algebra endowed with any group grading and any homogeneous involution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On star-homogeneous-graded polynomial identities of upper triangular matrices over an arbitrary field de Mello, Thiago Castilho Yasumura, Felipe Yukihide Rings and Algebras We study the graded polynomial identities with a homogeneous involution on the algebra of upper triangular matrices endowed with a fine group grading. We compute their polynomial identities and a basis of the relatively free algebra, considering an arbitrary base field. We obtain the asymptotic behaviour of the codimension sequence when the characteristic of the base field is zero. As a consequence, we compute the exponent and the second exponent of the same algebra endowed with any group grading and any homogeneous involution. |
| title | On star-homogeneous-graded polynomial identities of upper triangular matrices over an arbitrary field |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2402.02671 |