A linear algebra approach to graded Frobenius algebras
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909966463401984 |
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| author | Dascalescu, Sorin Nastasescu, Constantin Nastasescu, Laura Rebenciuc, Paul |
| author_facet | Dascalescu, Sorin Nastasescu, Constantin Nastasescu, Laura Rebenciuc, Paul |
| contents | If $A$ is a finite-dimensional algebra graded by a group $G$, and $σ\in G$, we define a variant of paratrophic matrix associated with $A$ and $σ$, and we use it to characterize the $σ$-graded Frobenius property for $A$. We discuss the invertibility of such paratrophic matrices, and then use them to check whether certain graded algebras are $σ$-graded Frobenius or (graded) symmetric. As an application, we uncover (graded) Frobenius and symmetric properties of Koszul duals of quantum polynomial algebras. We derive a structure result for $σ$-graded Frobenius algebras by only using linear algebra methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A linear algebra approach to graded Frobenius algebras Dascalescu, Sorin Nastasescu, Constantin Nastasescu, Laura Rebenciuc, Paul Rings and Algebras 16W50, 15A09, 16L60, 16S36, 16S37 If $A$ is a finite-dimensional algebra graded by a group $G$, and $σ\in G$, we define a variant of paratrophic matrix associated with $A$ and $σ$, and we use it to characterize the $σ$-graded Frobenius property for $A$. We discuss the invertibility of such paratrophic matrices, and then use them to check whether certain graded algebras are $σ$-graded Frobenius or (graded) symmetric. As an application, we uncover (graded) Frobenius and symmetric properties of Koszul duals of quantum polynomial algebras. We derive a structure result for $σ$-graded Frobenius algebras by only using linear algebra methods. |
| title | A linear algebra approach to graded Frobenius algebras |
| topic | Rings and Algebras 16W50, 15A09, 16L60, 16S36, 16S37 |
| url | https://arxiv.org/abs/2512.14852 |