Hidden structures behind ambient symmetries of the Maurer-Cartan equation
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908879554609152 |
|---|---|
| author | Dotsenko, Vladimir Shadrin, Sergey |
| author_facet | Dotsenko, Vladimir Shadrin, Sergey |
| contents | For every differential graded Lie algebra $\mathfrak{g}$ one can define two different group actions on the Maurer-Cartan elements: the ubiquitous gauge action and the action of $\mathrm{Lie}_\infty$-isotopies of $\mathfrak{g}$, which we call the ambient action. In this note, we explain how the assertion of gauge triviality of a homologically trivial ambient action relates to the calculus of dendriform, Zinbiel, and Rota-Baxter algebras, and to Eulerian idempotents. In particular, we exhibit new relationships between these algebraic structures and the operad of rational functions defined by Loday. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06589 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hidden structures behind ambient symmetries of the Maurer-Cartan equation Dotsenko, Vladimir Shadrin, Sergey Quantum Algebra Combinatorics Category Theory For every differential graded Lie algebra $\mathfrak{g}$ one can define two different group actions on the Maurer-Cartan elements: the ubiquitous gauge action and the action of $\mathrm{Lie}_\infty$-isotopies of $\mathfrak{g}$, which we call the ambient action. In this note, we explain how the assertion of gauge triviality of a homologically trivial ambient action relates to the calculus of dendriform, Zinbiel, and Rota-Baxter algebras, and to Eulerian idempotents. In particular, we exhibit new relationships between these algebraic structures and the operad of rational functions defined by Loday. |
| title | Hidden structures behind ambient symmetries of the Maurer-Cartan equation |
| topic | Quantum Algebra Combinatorics Category Theory |
| url | https://arxiv.org/abs/2407.06589 |