Projective resolutions of simple modules and Hochschild cohomology for incidence algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917355030839296 |
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| author | Bekkert, Viktor MacQuarrie, John William Marques, Júlio |
| author_facet | Bekkert, Viktor MacQuarrie, John William Marques, Júlio |
| contents | We give a practical, algorithmic method to calculate minimal projective resolutions of simple modules for a finite dimensional incidence $k$-algebra $Λ$, where $k$ is a field. We apply the method to the calculation of Ext groups between simple $Λ$-modules, Hochschild cohomology groups $\HH^i(Λ, Λ)$, and singular cohomology groups of finite $T_0$ topological spaces with coefficients in $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07910 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Projective resolutions of simple modules and Hochschild cohomology for incidence algebras Bekkert, Viktor MacQuarrie, John William Marques, Júlio Representation Theory Rings and Algebras 16E40, 16G20 We give a practical, algorithmic method to calculate minimal projective resolutions of simple modules for a finite dimensional incidence $k$-algebra $Λ$, where $k$ is a field. We apply the method to the calculation of Ext groups between simple $Λ$-modules, Hochschild cohomology groups $\HH^i(Λ, Λ)$, and singular cohomology groups of finite $T_0$ topological spaces with coefficients in $k$. |
| title | Projective resolutions of simple modules and Hochschild cohomology for incidence algebras |
| topic | Representation Theory Rings and Algebras 16E40, 16G20 |
| url | https://arxiv.org/abs/2411.07910 |