2-step Nilpotent $L_\infty$-algebras and Hypergraphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917595389624320 |
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| author | Aldi, Marco Bevins, Samuel |
| author_facet | Aldi, Marco Bevins, Samuel |
| contents | We describe a procedure to attach a nilpotent strong homotopy Lie algebra to every simple hypergraph and prove that two hypergraphs are isomorphic if and only if the corresponding strong homotopy Lie algebras are isomorphic. As an application, we characterize hypergraphs admitting a system of distinct representatives in terms of symplectic forms on the corresponding strong homotopy Lie algebra. We conclude with a combinatorial description of the cohomology of these strong homotopy Lie algebras in low degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13608 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | 2-step Nilpotent $L_\infty$-algebras and Hypergraphs Aldi, Marco Bevins, Samuel Combinatorics Differential Geometry Rings and Algebras We describe a procedure to attach a nilpotent strong homotopy Lie algebra to every simple hypergraph and prove that two hypergraphs are isomorphic if and only if the corresponding strong homotopy Lie algebras are isomorphic. As an application, we characterize hypergraphs admitting a system of distinct representatives in terms of symplectic forms on the corresponding strong homotopy Lie algebra. We conclude with a combinatorial description of the cohomology of these strong homotopy Lie algebras in low degree. |
| title | 2-step Nilpotent $L_\infty$-algebras and Hypergraphs |
| topic | Combinatorics Differential Geometry Rings and Algebras |
| url | https://arxiv.org/abs/2212.13608 |