The Hochschild cohomology ring of monomial algebras
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917673856663552 |
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| author | Artenstein, Dalia Letz, Janina C. Oswald, Amrei Solotar, Andrea |
| author_facet | Artenstein, Dalia Letz, Janina C. Oswald, Amrei Solotar, Andrea |
| contents | We give an explicit description of a diagonal map on the Bardzell resolution for any monomial algebra, and we use this diagonal map to describe the cup product on Hochschild cohomology. Then, we prove that the cup product is zero in positive degrees for triangular monomial algebras. Our proof uses the graded-commutativity of the cup product on Hochschild cohomology and does not rely on explicit computation of the Hochschild cohomology modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14699 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Hochschild cohomology ring of monomial algebras Artenstein, Dalia Letz, Janina C. Oswald, Amrei Solotar, Andrea Representation Theory 16E40 (primary), 18G10 We give an explicit description of a diagonal map on the Bardzell resolution for any monomial algebra, and we use this diagonal map to describe the cup product on Hochschild cohomology. Then, we prove that the cup product is zero in positive degrees for triangular monomial algebras. Our proof uses the graded-commutativity of the cup product on Hochschild cohomology and does not rely on explicit computation of the Hochschild cohomology modules. |
| title | The Hochschild cohomology ring of monomial algebras |
| topic | Representation Theory 16E40 (primary), 18G10 |
| url | https://arxiv.org/abs/2312.14699 |