Algebras with additional structures and multiplicities bounded by a constant
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909823819317248 |
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| author | Santos, R. B. dos Vieira, A. C Vieira, R. F. D. N. |
| author_facet | Santos, R. B. dos Vieira, A. C Vieira, R. F. D. N. |
| contents | $G$ be a finite group and $A$ a $G$-graded algebra over a field $F$ of characteristic zero. We characterize the varieties of $G$-graded algebras such that the multiplicities $m_{\langle λ\rangle}$ appering in the $\langle n \rangle $-cocharacters of $A$ are bounded by a constant, in terms of $G$-identities. If $A$ is endowed with a graded involution $\ast$, i.e. if $A$ is a $(G,\ast)$-algebra, we characterize the varieties of $(G,*)$-algebras whose multiplicities in the sequence of $\langle n\rangle$-cocharacters of $A$ are bounded by $1$ by showing a list of $(G,\ast)$-polynomial identities satisfied by such varieties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_03583 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebras with additional structures and multiplicities bounded by a constant Santos, R. B. dos Vieira, A. C Vieira, R. F. D. N. Rings and Algebras Primary 16R10, 16R50, Secondary 16W10, 16W50, 20C30 $G$ be a finite group and $A$ a $G$-graded algebra over a field $F$ of characteristic zero. We characterize the varieties of $G$-graded algebras such that the multiplicities $m_{\langle λ\rangle}$ appering in the $\langle n \rangle $-cocharacters of $A$ are bounded by a constant, in terms of $G$-identities. If $A$ is endowed with a graded involution $\ast$, i.e. if $A$ is a $(G,\ast)$-algebra, we characterize the varieties of $(G,*)$-algebras whose multiplicities in the sequence of $\langle n\rangle$-cocharacters of $A$ are bounded by $1$ by showing a list of $(G,\ast)$-polynomial identities satisfied by such varieties. |
| title | Algebras with additional structures and multiplicities bounded by a constant |
| topic | Rings and Algebras Primary 16R10, 16R50, Secondary 16W10, 16W50, 20C30 |
| url | https://arxiv.org/abs/2510.03583 |