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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.01798 |
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| _version_ | 1866908398378811392 |
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| author | Koç, Ayten Özaydın, Murad |
| author_facet | Koç, Ayten Özaydın, Murad |
| contents | We provide a complete answer to the question "When is a quotient of a Leavitt path algebra isomorphic to a Leavitt path algebra?" in terms of the interaction of the kernel of the quotient homomorphism with the cycles of the digraph. A key ingredient is the characterization of finitely generated projective (Leavitt path algebra) modules whose endomorphism algebras are finite dimensional. As a consequence of our characterization we get that any quotient of a Leavitt path algebra divided by its Jacobson radical is a Leavitt path algebra if the coefficient field is large enough. We define a stratification and a parametrization of the ideal space of a Leavitt path algebra (initially in terms of the digraph, later algebraically) and show that a generic quotient of a Leavitt path algebra is a Leavitt path algebra. Contrary to most algebraic properties of Leavitt path algebras, our criterion for a quotient to be isomorphic to a Leavitt path algebra is not independent of the field of coefficients. We end this article by pointing out a connection with quantum spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generic Quotient of a Leavitt Path Algebra is a Leavitt Path Algebra Koç, Ayten Özaydın, Murad Rings and Algebras 16S88 We provide a complete answer to the question "When is a quotient of a Leavitt path algebra isomorphic to a Leavitt path algebra?" in terms of the interaction of the kernel of the quotient homomorphism with the cycles of the digraph. A key ingredient is the characterization of finitely generated projective (Leavitt path algebra) modules whose endomorphism algebras are finite dimensional. As a consequence of our characterization we get that any quotient of a Leavitt path algebra divided by its Jacobson radical is a Leavitt path algebra if the coefficient field is large enough. We define a stratification and a parametrization of the ideal space of a Leavitt path algebra (initially in terms of the digraph, later algebraically) and show that a generic quotient of a Leavitt path algebra is a Leavitt path algebra. Contrary to most algebraic properties of Leavitt path algebras, our criterion for a quotient to be isomorphic to a Leavitt path algebra is not independent of the field of coefficients. We end this article by pointing out a connection with quantum spaces. |
| title | A Generic Quotient of a Leavitt Path Algebra is a Leavitt Path Algebra |
| topic | Rings and Algebras 16S88 |
| url | https://arxiv.org/abs/2503.01798 |