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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.12396 |
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| _version_ | 1866912056154783744 |
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| author | Fuentes, Mario |
| author_facet | Fuentes, Mario |
| contents | In an arbitrary complete differential graded Lie algebra, we construct a group operation $\bullet$ on $L_1$ such that the differential of the product of two elements is the Baker-Campbell-Hausdorff product of their differentials, i.e., $d(x\bullet y)=dx\ast dy$. We study some properties of this new structure and some applications, especially in homotopy theory, where this operation can be used to construct a Lie model for the 4-simplex. In particular, this solves, in dimension 4, a problem proposed by Lawrence and Sullivan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12396 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integration of the Baker-Campbell-Hausdorff product Fuentes, Mario Algebraic Topology Rings and Algebras In an arbitrary complete differential graded Lie algebra, we construct a group operation $\bullet$ on $L_1$ such that the differential of the product of two elements is the Baker-Campbell-Hausdorff product of their differentials, i.e., $d(x\bullet y)=dx\ast dy$. We study some properties of this new structure and some applications, especially in homotopy theory, where this operation can be used to construct a Lie model for the 4-simplex. In particular, this solves, in dimension 4, a problem proposed by Lawrence and Sullivan. |
| title | Integration of the Baker-Campbell-Hausdorff product |
| topic | Algebraic Topology Rings and Algebras |
| url | https://arxiv.org/abs/2405.12396 |