Group graded algebras and varieties with quadratic codimension growth
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917237969911808 |
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| author | Cota, Wesley Quaresma |
| author_facet | Cota, Wesley Quaresma |
| contents | Let $A$ be an associative algebra graded by a finite group $G$ over a field ${F}$ of characteristic zero. One associates to $A$ the sequence of $G$-graded codimensions $c_n^G(A)$, $n=1,2,\ldots$, which measures the growth of the polynomial identities satisfied by $A$. It is known that this sequence is either polynomially bounded or grows exponentially. In this paper, we study unitary $G$-graded varieties of polynomial codimension growth. In particular, we classify the varieties generated by unitary algebras with quadratic codimension growth and show that these varieties can be described as a direct sums of algebras that generate minimal $G$-graded varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Group graded algebras and varieties with quadratic codimension growth Cota, Wesley Quaresma Rings and Algebras Primary 16R10, 16W50, Secondary 20C30 Let $A$ be an associative algebra graded by a finite group $G$ over a field ${F}$ of characteristic zero. One associates to $A$ the sequence of $G$-graded codimensions $c_n^G(A)$, $n=1,2,\ldots$, which measures the growth of the polynomial identities satisfied by $A$. It is known that this sequence is either polynomially bounded or grows exponentially. In this paper, we study unitary $G$-graded varieties of polynomial codimension growth. In particular, we classify the varieties generated by unitary algebras with quadratic codimension growth and show that these varieties can be described as a direct sums of algebras that generate minimal $G$-graded varieties. |
| title | Group graded algebras and varieties with quadratic codimension growth |
| topic | Rings and Algebras Primary 16R10, 16W50, Secondary 20C30 |
| url | https://arxiv.org/abs/2512.06153 |