Universal constructions in homotopical algebra
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912637665673216 |
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| author | Campos, Ricardo Vallette, Bruno |
| author_facet | Campos, Ricardo Vallette, Bruno |
| contents | We apply the effective integration theory of Lie-graph algebras, developed recently by the authors, to the deformation and homotopy theories of types of bialgebras, that is structures controlled by a properad, like associative bialgebras, (involutive) Lie bialgebras, Frobenius bialgebras, double Poisson bialgebras, pre-Calabi--Yau algebras, quantum Airy structures, etc. In these cases, we provide their associated Deligne groupoid with an explicit homotopical description. We settle the Koszul hierarchy and the twisting procedure on the properadic level. We also give a conceptual construction of the homotopy transfer theorem in terms of gauge actions. This work extends the formulas for the deformation theory of operadic algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal constructions in homotopical algebra Campos, Ricardo Vallette, Bruno Quantum Algebra Mathematical Physics Primary 18M85, Secondary 14D15, 16T10, 18M70, 22E65 We apply the effective integration theory of Lie-graph algebras, developed recently by the authors, to the deformation and homotopy theories of types of bialgebras, that is structures controlled by a properad, like associative bialgebras, (involutive) Lie bialgebras, Frobenius bialgebras, double Poisson bialgebras, pre-Calabi--Yau algebras, quantum Airy structures, etc. In these cases, we provide their associated Deligne groupoid with an explicit homotopical description. We settle the Koszul hierarchy and the twisting procedure on the properadic level. We also give a conceptual construction of the homotopy transfer theorem in terms of gauge actions. This work extends the formulas for the deformation theory of operadic algebras. |
| title | Universal constructions in homotopical algebra |
| topic | Quantum Algebra Mathematical Physics Primary 18M85, Secondary 14D15, 16T10, 18M70, 22E65 |
| url | https://arxiv.org/abs/2510.06941 |