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| Format: | Preprint |
| Publié: |
2020
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2002.00886 |
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| _version_ | 1866916164368596992 |
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| author | Hawkins, Eli |
| author_facet | Hawkins, Eli |
| contents | A diagram of algebras is a functor valued in a category of associative algebras. I construct an operad acting on the Hochschild bicomplex of a diagram of algebras. Using this operad, I give a direct proof that the Hochschild cohomology of a diagram of algebras is a Gerstenhaber algebra. I also show that the total complex is an $L_\infty$-algebra. The same results are true for the reduced and asimplicial subcomplexes and asimplicial cohomology. This structure governs deformations of diagrams of algebras through the Maurer-Cartan equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_00886 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Operations on the Hochschild Bicomplex of a Diagram of Algebras Hawkins, Eli Category Theory Algebraic Topology Rings and Algebras 18D50 (primary) 16E40 (Secondary) A diagram of algebras is a functor valued in a category of associative algebras. I construct an operad acting on the Hochschild bicomplex of a diagram of algebras. Using this operad, I give a direct proof that the Hochschild cohomology of a diagram of algebras is a Gerstenhaber algebra. I also show that the total complex is an $L_\infty$-algebra. The same results are true for the reduced and asimplicial subcomplexes and asimplicial cohomology. This structure governs deformations of diagrams of algebras through the Maurer-Cartan equation. |
| title | Operations on the Hochschild Bicomplex of a Diagram of Algebras |
| topic | Category Theory Algebraic Topology Rings and Algebras 18D50 (primary) 16E40 (Secondary) |
| url | https://arxiv.org/abs/2002.00886 |