Categorification of quiver diagonalization and Koszul algebras
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911780215717888 |
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| author | Dotsenko, Vladimir Feigin, Evgeny Kucharski, Piotr Reineke, Markus |
| author_facet | Dotsenko, Vladimir Feigin, Evgeny Kucharski, Piotr Reineke, Markus |
| contents | In earlier work of three of the authors of the present paper, a supercommutative quadratic algebra was associated to each symmetric quiver, and a new proof of positivity of motivic Donaldson-Thomas invariants of symmetric quivers was given using the so called numerical Koszul property of these algebras. It was furthermore conjectured that for each symmetric quiver such an algebra is Koszul. In this work, we lift the linking and unlinking operations on symmetric quivers of Ekholm, Longhi and the third author to the level of quadratic algebras, and use those lifts to prove the Koszulness conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12768 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Categorification of quiver diagonalization and Koszul algebras Dotsenko, Vladimir Feigin, Evgeny Kucharski, Piotr Reineke, Markus Representation Theory Algebraic Geometry K-Theory and Homology Quantum Algebra Rings and Algebras In earlier work of three of the authors of the present paper, a supercommutative quadratic algebra was associated to each symmetric quiver, and a new proof of positivity of motivic Donaldson-Thomas invariants of symmetric quivers was given using the so called numerical Koszul property of these algebras. It was furthermore conjectured that for each symmetric quiver such an algebra is Koszul. In this work, we lift the linking and unlinking operations on symmetric quivers of Ekholm, Longhi and the third author to the level of quadratic algebras, and use those lifts to prove the Koszulness conjecture. |
| title | Categorification of quiver diagonalization and Koszul algebras |
| topic | Representation Theory Algebraic Geometry K-Theory and Homology Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2402.12768 |