Polyhedral products, graph products and p-central series
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912190008655872 |
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| author | Panov, Taras Rahmatullaev, Temurbek |
| author_facet | Panov, Taras Rahmatullaev, Temurbek |
| contents | We relate polyhedral products of topological spaces to graph products of groups. The loop homology algebras of polyhedral products are identified with the universal enveloping algebras of the Lie algebras associated with central series of graph products. By way of application, we describe the restricted Lie algebra associated with the lower 2-central series of a right-angled Coxeter group and identify its universal enveloping algebra with the loop homology of the Davis-Januszkiewicz space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polyhedral products, graph products and p-central series Panov, Taras Rahmatullaev, Temurbek Algebraic Topology Group Theory Rings and Algebras 16S10, 17B35, 20F40, 20F65, 55P35, 57M07, 57S12 We relate polyhedral products of topological spaces to graph products of groups. The loop homology algebras of polyhedral products are identified with the universal enveloping algebras of the Lie algebras associated with central series of graph products. By way of application, we describe the restricted Lie algebra associated with the lower 2-central series of a right-angled Coxeter group and identify its universal enveloping algebra with the loop homology of the Davis-Januszkiewicz space. |
| title | Polyhedral products, graph products and p-central series |
| topic | Algebraic Topology Group Theory Rings and Algebras 16S10, 17B35, 20F40, 20F65, 55P35, 57M07, 57S12 |
| url | https://arxiv.org/abs/2402.11556 |