Integration theory of Lie-graph algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916997763170304 |
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| author | Campos, Ricardo Vallette, Bruno |
| author_facet | Campos, Ricardo Vallette, Bruno |
| contents | We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce effective formulas for their exponential map, their gauge group structure and the action on Maurer--Cartan elements. The main motivation and range of applications lies in the deformation theory of types of bialgebras which is done in a sequel article. This work extends the case of pre-Lie algebra structures which appear in the deformation theory of operadic algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06934 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integration theory of Lie-graph algebras Campos, Ricardo Vallette, Bruno Quantum Algebra Primary 22E65, Secondary 18M70, 18M85, 14D15, 16T10 We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce effective formulas for their exponential map, their gauge group structure and the action on Maurer--Cartan elements. The main motivation and range of applications lies in the deformation theory of types of bialgebras which is done in a sequel article. This work extends the case of pre-Lie algebra structures which appear in the deformation theory of operadic algebras. |
| title | Integration theory of Lie-graph algebras |
| topic | Quantum Algebra Primary 22E65, Secondary 18M70, 18M85, 14D15, 16T10 |
| url | https://arxiv.org/abs/2510.06934 |