Quivers with Polynomial Identities
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911132846915584 |
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| author | Irelli, Giovanni Cerulli Chávez, Javier De Loera Pascucci, Elena |
| author_facet | Irelli, Giovanni Cerulli Chávez, Javier De Loera Pascucci, Elena |
| contents | We provide a topological characterization of quivers whose path algebra satisfies a polynomial identity. This class includes the oriented cycle and acyclic quivers and, in the latter case, we describe the associated T-ideal. We introduce a generalization of Arnold's A-graded algebras, which we call locally A-graded algebras, and prove that they are also PI. We give an example of a quiver algebra satisfying a polynomial identity, even if the path algebra of the quiver does not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quivers with Polynomial Identities Irelli, Giovanni Cerulli Chávez, Javier De Loera Pascucci, Elena Representation Theory Combinatorics Rings and Algebras We provide a topological characterization of quivers whose path algebra satisfies a polynomial identity. This class includes the oriented cycle and acyclic quivers and, in the latter case, we describe the associated T-ideal. We introduce a generalization of Arnold's A-graded algebras, which we call locally A-graded algebras, and prove that they are also PI. We give an example of a quiver algebra satisfying a polynomial identity, even if the path algebra of the quiver does not. |
| title | Quivers with Polynomial Identities |
| topic | Representation Theory Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2508.00662 |