The Derived Deligne Conjecture
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929509995905024 |
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| author | Martín, Javier Aguilar Roitzheim, Constanze |
| author_facet | Martín, Javier Aguilar Roitzheim, Constanze |
| contents | Derived $A_\infty$-algebras have a wealth of theoretical advantages over regular $A_\infty$-algebras. However, due to their bigraded nature, in practice they are often unwieldy to work with. We develop a framework involving brace algebras on operads which allows us to study derived $A_\infty$ algebras in a new conceptual context. One particular advantage is that this construction allows us to generalize the Lie algebra structure on the Hochschild complex of an $A_\infty$-algebra, obtaining new and rigorous versions of the Deligne conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11414 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Derived Deligne Conjecture Martín, Javier Aguilar Roitzheim, Constanze Rings and Algebras 18M70, 18M60, 18N70 Derived $A_\infty$-algebras have a wealth of theoretical advantages over regular $A_\infty$-algebras. However, due to their bigraded nature, in practice they are often unwieldy to work with. We develop a framework involving brace algebras on operads which allows us to study derived $A_\infty$ algebras in a new conceptual context. One particular advantage is that this construction allows us to generalize the Lie algebra structure on the Hochschild complex of an $A_\infty$-algebra, obtaining new and rigorous versions of the Deligne conjecture. |
| title | The Derived Deligne Conjecture |
| topic | Rings and Algebras 18M70, 18M60, 18N70 |
| url | https://arxiv.org/abs/2307.11414 |